1. I'm assuming close contact to earth is optimal, but will my magic suffer if I'm for instance, trying to cast from the stone floor of a castle or the wooden floor of a tavern, both of which are connected to the ground indirectly? What if I'm on the deck of a ship-could I reach the seafloor, or nearby coral beds with enough skill?
There needs to be a conduit of nature for your entire ability to be successful - Where electricity can only travel down an adequate conductor, geomancy is the same. If you're stood on a stone floor you are able to manipulate the stones and your magic mapping works by sensing where stones are in proximity to eachother, thereby creating a three-dimensional map in your head. This means you're able to detect traps embedded in rock, trapped wooden doors etc.
This means that if you're on a wooden ship you'll be able to manipulate the wood as a basic spell. As an intermediate spell you'd be able to use the natural wood as a conduit to the water and sense nearby underwater features in a manner similar to sonar. As an advanced spell you'd be able to use the wood AND water as a conduit but your power to manipulate the sea floor would be limited. As a legendary spell, you could manipulate the sea floor as if you were physically stood on it. As a godlike spell you could even channel the life-force of your party through the wood on a boat, then through the sea onto the sea floor. You could then manipulate the water to forcefully raise a sunken treasure chest by generating upward currents.
At your basic skill level you're restricted to only rocks, dirt and wood/trees/plantlife. As you advance you'll be able to use water as a conduit, then eventually manipulate it. At an extremely high level you'll also be able to supress magma/lava in order to walk over it.
Geomancy is a physical caster school so you can only do physical effects with things that already exist. You can stimulate vines to grow up through soil, you can manipulate a spear into striking up from the Earth - Eventually you could create waves in a pond or fill a well by forcing water out of soil in the ground near the well. But you can never conjure from what does not already exist.
But what were to happen if you were to find training in a mental spell school? With geomancy you can eventually learn to control water that physically exists. But if you were to learn a skill like Magic [Air] to a sufficient level you may be able to use air as a conduit for your geomancy (and thus use geomancy while flying) - Or combine it to create a stone spear using geomancy and thrust it using air magic. If you learned Magic [Water] you could transform an area of stone to mud. If your Magic [Water] and skill was high enough you could then freeze the mud.
2. Could I carry a jar of Earth around with me to cast spells when I'm out of my element, or gather up all the grit and stones in a radius around me to cast an admittedly weak spell?
I may have already mentioned this above - Yes, it's fully possible but a geomancer can not conjure, they can only cultivate. In order to summon a stone spear you must take a little bit of everything around you - This will weaken the nearby materials. Vines are grown by stimulating them to absorb water from the Earth, if there Earth is too dry you will fail.
That isn't to say you're completely useless though. If you work with your party you can create combination attacks that use the skills of multiple players. A geomancer can turn even a small stone into dust which is made of super-sharp particles. This dust can than be used by a party member who is capable of manipulating air to blast a dust cloud in an attempt to weaken an enemy's vision. And that's a powerful combination usable by (no-adjective) geomancers and air magic users.
Alternatively - If you carried a stone block about the size of a brick with you, it's fully possible you could mould it around your hand and enhance your physical punches by turning them into geomancy empowered stone strikes.
3. Does Geomancy extend to every natural thing I could find in the Earth? To give another example, if there is oil under me, I could blind my enemies with oil spray, or could I animate a dinosaur fossil to fight for me heh heh.
Bones can be used as part of geomancy, although animating a dinosaur fossil may not be immensely effective as you'd need to channel in order to do so and you'd exert an immense amount of your energy in physically raising the bones up from the floor (since you'd need to make dirt act like water and "flow" to allow each bone to be pushed up to the surface) - But when your skill gets high enough you could animate and control a rock golem - Again, same limitations: You can't give your golem sentient life so once you stop focusing on the task it would just collapse into it's component parts.
As for liquids, they're advanced geomancy as they require a whole new level of skill to manipulate. If you start to craft a stone spear from the floor and you stop halfway through, the stone spear would be half complete. Now if you tried a similar task with a liquid and stopped halfway through, the liquid would just disperse. If you wanted to accomplish this task without being skillful enough to manipulate the oil you'd need to push the oil to the surface then create a localised, powerful ground tremor that would project the oil at the opponent. Or team up with a Magic [Air] user. Or learn Magic [Air].
The strength with your geomancy is - Again - It's a physical caster school so it drains your physical energy. It's as if you're manipulating things with your own bare hands. This means that only half your character's potential is used - Pick up Magic [Air] and you can use your physical Geomancy to craft a spear, then use your mental Air to blast it and it won't double-exhaust your physical strength.
But don't worry, your opponents will be using any combination effects they are capable of from my own imagination against you - So you'll get plenty of ideas as you progress through the campaigns!