Sometimes a piece of the ocean floor (called a plate) will form a crack, and one side of the crack will sink beneath the other side. As the sinking side falls into the Earth’s mantle below, it pulls the rest of its plate with it. The ocean floor deepens along this crack. The sinking seafloor grinds against the other side of the crack and tears pieces off to be carried down into the Earth. The overall result is a long, deep trench that marks the location of the initial crack. We call such features subduction zones or oceanic trenches. This process is how the Mariana Trench formed.

This is a tricky question, partly because the word "highest" can have several definitions in the context of ocean floor geology, and partly because of the complexity of seafloor spreading processes.

If you define "highest" as the shallowest water depth at which a rift valley or spreading center exists, the winner would be the Mid Atlantic Ridge (MAR). Some of the underwater mountains created along this rift valley lie at only ~500 meters water depth.

If you define "highest" as the greatest distance between the shallowest point on the ridge and the deepest point (the elevation of the ridge), the winner would again be the MAR. There are places — usually at the intersection of the ridge and a transform fault — on the MAR where there is a 6000 meter elevation change.

If you define "highest" as the average ridge height compared to the average seafloor depth, the winner would be the Southern Eastern Pacific Ridge (SEPR) in the South Pacific Ocean. This is because the SEPR is a very active volcanic ridge that builds mountains, whereas the MAR is an earthquake-prone area that creates large valleys.

There are many similarities between underwater volcanic eruptions and eruptions on land, but it is unlikely that an event like Mt. St. Helens would occur at the seafloor. Most often eruptions are due to a dikes (very large vertical sheets of lava) which break through to the surface of the ocean floor. Often this results in lava oozing out onto the seafloor and creating new seafloor. The outer crust of newly erupted lava hardens instantly, creating a cool shell that sometimes allows liquid lava to exist on the inside. Many times flowing lava ultimately recedes, leaving just the hardened shell — a very common formation known as a lava tube.

Animals don’t live inside of volcanoes, but they do live on the rocks on a volcano’s outer surface. No giant squid have been reported yet, but a large number of unique and strange-looking animals live near the seafloor. Tiny shrimp-like creatures, worms, sea cucumbers and fish live at the bottom of all oceans, and animals such as tube worms, sea anemones, rays, octopi, certain deep-sea fish and giant crabs are unique to hydrothermal vents areas on volcanoes.

California is the state with the longest continuous stretch of continental shelf, which is off the coast of the continent itself. However, states like Alaska have many more miles of coastline than California.

If a trench suddenly forms a great deal of water does fill in the new volume created. However, the volume of the ocean is so great that the water filling in the trench is miniscule in comparison. Without doing any calculation, I would guess that if a new trench formed that is larger than the largest trench in the ocean, the ocean level might drop less than a millimeter. Also, the earth is in a "steady state," meaning that for every trench formed, on average there is an equal volume of seafloor mountains created, and thus there would be no overall change in ocean volume.

In the past oceanographers would hang a big weight over the side of a ship and let it sink until it hit the bottom (when it hits the bottom there would be a change in the tension of the line). The oceanographers would know how much line they had let out, and thus the depth. These types of measurements are much more sophisticated today. Depth measurements can be made very accurately (within millimeters) by pressure sensors lowered to the bottom. However, the most common technique for determining "bathymetry" (ocean floor topography, and hence depth) is with acoustic techniques, usually referred to as Sea Beam. The Sea Beam works much like a bat’s or a dolphin’s echolocation. The ship sends out a high pitched signal which bounces of the seafloor and is received by a sensor on the bottom of the ship. The deeper the ocean is, the longer the signal will take to travel to the seafloor and back. A computer onboard crunches all the numbers and makes a color map of seafloor depths.

Hawaii. If you think of the Mauna Kea volcano as extending from the seafloor — not just from sea level — then it is much larger than Mount Everest, and would be considered the largest volcano on earth. There are other volcanoes being built just off the coast of Hawaii that are currently underwater, but give them a couple hundred thousand years and they will break the surface of the ocean. The most popular one is called Loihi and is a site of a active research.

The biggest effect of oil that escapes from a drilling site is probably on animals that inhabit the surface of the ocean. Since oil is buoyant, it quickly rises to the surface and floats there. It is sticky, too, so it tends to accumulate on sea birds and mammals. Once in the feathers and fur, it mats the animal’s natural insulation down and causes them to freeze to death. Bird feathers aren’t good for flying when they’re covered in oil. Closer to shore, the floating oil can have big impacts on the animals and people who use the beaches. In Southern California, you have to clean your feet after walking on the beach.

Yes!! It can happen, especially if they are in the way of a lava flow. Just such an event happened at 9°N latitude on the East Pacific Rise in the Pacific Ocean where a new lava flow covered and cooked a cluster of tube worms and killed them. This area was known as the "Tube Worm Barbeque" site. Fortunately, within a year or two after the eruption, new worms had already come in to colonize the seafloor.

Very simply, yes, and drastically. Eruptions, in addition to creating most of the seafloor geology we observe (until it is covered by sediments), do a lot to the biology and microbiology of the ocean. Many times eruptions destroy biology that has been living in hydrothermal vent areas. But more often than not, eruptions flush the habitats beneath the seafloor of any microbiology living within the crust, allowing these microorganisms to find new homes, and colonize new areas. Also volcanic eruptions may create new areas of hydrothermal activity, and thus new homes to many different types of animals.

The smallest trench would be one that had recently formed — though I’m not sure which trench is the youngest. As you can see all around the edge of the Pacific Ocean, most trenches are over two miles deep.

Some seamounts are forming through volcanic eruptions right now. A good example is Loihi, the newest addition to the Hawaiian seamount chain. If you follow the Hawaiian chain westward, you will see older and older seamounts. While Loihi has not yet grown above sea level, the state of Hawaii is made up of seamounts that have become islands.

With three pieces of information you can calculate the age of the oldest Hawaiian island: the Pacific plate is moving over the Hawaiian hot spot at a relative speed of about 30 kilometers per million years (My); the hot spot is basically underneath Loihi right now; the distance from Loihi to the oldest island is about 900 km. So, the oldest island is about (900 km / 30 km/My = ) 30 million years old.

The Hawaiian chain continues west for about ~2100 kilometers and then connects to the Emperor seamount chain that extends ~2100 kilometers, all the way to the Aleutian trench. Assuming the same relative speed has been maintained during their formation, the oldest seamounts in the Hawaiian and Emperor chains have ages of about (2100 km / 30 km/My = ) 70 My and (4200/30 = ) 140 My, respectively. Midway island must have been a really big seamount because it is about 1500 km west of Loihi and still hasn’t subsided below sea level, even after ~50 My.

Perhaps a better way to phrase you question is "How did the continental shelf form?" It’s an excellent question you’ve asked, and here’s one possible answer.

First imagine the situation when a new continent is formed, but without an ocean present. The rock that makes up the continent is thicker and less dense than that which makes up the ocean floor, so the continent floats relatively higher on the Earth’s molten mantle. Big volcanoes on the continent spew out more low-density rock and the continent gets some nice steep sides.

Now fill up the low areas (ocean floor) with a bunch of sea water and energize the surface of the resultant seas with lots of wind. Big waves form on the oceans’ surface and travel across the basins to the continental shores. There they crash into the fresh continental rock and begin to break away pieces. Eventually the waves tear away the edge of the continent as fast as the continental volcanoes can create it. So the continent now has even steeper sides and a bit of a shelf where the waves have broken off rock and washed it down the submarine slopes into the basins.

Now add some ice caps to the planet and alternate between big ice caps during ice ages and no ice caps during warm periods. During the ice ages, lots of the sea water ends up frozen in big piles on the caps. This mean the sea level decreases during these periods. Thus, the waves are still at work on the continent, but lower down on the slope now. So, the small shelf gets wider as the lower continental rocks are worn away into the deep. Along with the changing sea level, the width and relative elevation of the continental shelf changes. In some special places (where the continent happened to be rising up during such climatic changes) multiple shelves were created, and are now preserved for us to study high above the present sea level.

They form when the Earth’s seafloor tears apart (because it is denser than the underlying mantle and is always trying to sink into it). The tear decreases the pressure in the molten rock below, causing it to create lots of buoyant liquid rock. The liquid rock is called "magma" and once it has risen through the mantle to the tear in the seafloor, it erupts and is termed "lava." The lava fills up the tear, and even piles up above it to form the long, linear underwater volcanoes we call oceanic ridges.

Other submarine volcanoes form above "hot spots" in the Earth’s mantle. These are like hot blisters which burst through the ocean crust. Hawaii is an example of a hot spot volcano.

Water pressure doesn’t crush sediments because the spaces between sediment particles (called "pores") are themselves filled with water. Because sediments have these pores, they adjust to the changes in water pressure that occur as you go deeper in the ocean. Imagine that sediments are composed of a snow-like material. As the snowflakes pile up on top of each other, they leave little empty pockets between them. These pockets of water are not confined in any way (like the water inside of a fish), and so there is nothing to crush.