Answering what I can:
* Keas come into my fort and steal crap, can I create a safe or a vault that protects my most valuable stuff?
Sure, in theory. You can set up stockpiles deep inside of your fort that keas and other thieving creatures would have a hard time reaching without being spotted and run off. Cage traps will catch a lot of things, and are probably one of the best things to try. If a dwarf can reach it though, it's theoretically not completely safe.
* I have a swarm of war dogs pastured at the entrance of my fort, how can keas and other thieves get into my fort?
That should help a lot to keep them out, but depending on the entrance layout and how many dogs you have there it's possible that they wandered far enough from the entrance that something could sneak by. Have you tried chaining them there instead of pasturing them?
* I'm trying to get some magma going to replace the lost wood, but I've heard bad things happen if I dig too greedily and too deep. How far down do I have to go? I'm at -110, but I've encountered hot walls a couple places higher up. If I dig into these hot spots will I risk flooding my fort with liquid death?
Usually you don't find that kind of Fun by accident (though it happens), so it's relatively safe to dig down if you're methodical about it. The biggest thing when it comes to digging for magma is that it works like water and is pressurized, so you want to try to tap into it at the highest level possible, else it may surprise you with how it flows and floods upward.
* Are genetics a thing in the game? I've been singling out my best males and making them studs and gelding the rest. Am I wasting my time? Or is it best practice to breed my best pairs?
Genetics are a thing. I'm not sure how much it actually matters for size, stats and so on so I can't comment on the viability of using it for things like improving your food industries, but it is a thing you can do. It also influences appearance for creatures, which mostly matters for intelligent creatures like dwarves.
* My computer isn't the newest so I'm limiting my fort to 40. We just had a baby. Are we going to have to care for this poop machine for 18 years before they are worth a damn?
Yes and no. Once they're a year old and no longer a baby they'll do the new chores tasks, but that's mostly hauling and I think some farming tasks. Unfortunately, they can't do regular tasks until they're adults though, which does happen at 18 years old now.