Certain races have buildings specific to them. For instance the Armory is exclusive to Dwarf and Fighter. Currently I'm operating under the assumption that the armory will only provide this bonus to that race. If this is in error, please let me know. If, however, I build and armory and transfer ownership to, say, Elves or Halflings, would they then gain the bonuses of the Armory? (This question extends to other racial buildings like the Bakery, the Forge, etc.)

What is the best way to train units? Should you place units you're training in the same area as the building that provides the bonus (for example, the Temple for Cleric's), or should you just build a bunch of them, set the triangle to full "Train" and let it ride? Is there a cap on the bonus these buildings will provide?

Does the race of your stronghold leader have a significant impact on the game?

Your Baron's race doesn't matter that much. Different classes have different costs/stats for keeps so there is a small min/max game you can play early on. I prefer a dwarf as my Baron for the mining and building bonuses (I usually start up in the mountains) but I'd pick based on the class you want to with rather than on the costs of the keep. As I recall the cleric is considered to have the best keep so some players prefer not to make their cleric the Baron.

For training, each training building provides a training boost on a per-unit basis (so one training facility trains 1 unit per turn, 2 facilities train 2 units per turn, and so on) You don't need to keep units you are training on the same tile as your facility but you can collect your units on one tile and set that tile to 100% training to help.

For gear armories are good for each class except mages (so you build them with your fighter/dwarf and transfer ownership). Mages can build apothecaries that can cause gear to improve by +1 and this is how you get +3 weapons for your troops. For Mage armor, Mages need rings (which they can build) that improve their armor.

That's what I needed to know. Thank you for the response.