I can't really answer question #1 as I've never built an animation system, nor have I really exported anything to run in an existing system, but I'll do my best for the other two.
For AI, every certain number of frames or a timeslice of every frame (or every frame without a timeslice, whatever), you'll want to manage your AI's thought process. Make decisions on what they want to do based on whatever number of influences. Then every frame, make sure you're updating what they're actually doing, whether it be moving, or updating the progress of a building they're creating, or attacking, etc... This can be done on a separate thread, just make sure everything they're doing is based on time and not frames.
For a game engine, that's a seriously loaded question. A game engine will encompass everything from timekeeping to rendering to math operations to a whole bunch of stuff. Take a look on Amazon for the sample of 3D Game Engine Architecture by Eberly. That will give you a basic rundown of what subsystems you'll encounter when rolling your own engine.
I'm not familiar with Blender's engine, so I can't really go into detail about that, but Unity is a very popular engine with a very slick toolset. There's gobs of tutorials out there for that. I'm assuming Blender works somewhat on the same lines as Unity.
If you're looking for a basic 3D engine without all the bells & whistles of Blender, Unity or Torque, Ogre3D is a nice one that I've used a bit. If you want even less than that and want to roll your own, you're in for a lot of work.
Finally, if you're brand new to game development, 3D is a very big step into that world. Try out 2D if you want to get the basics of how to write a game framework and something simple, then build up to 3D.
Hope that all helps you in your quest! Best of luck and hopefully you'll make it out alive ;)