Was wondering if the sequel improves/changes any of these things that bothered me about the first one:
-Research is set to a pre-determined order - answered
-Some traps and spells aren't very useful? (gas trap, cave-in) - answered?
-Training takes too long - answered?

-No box selecting/select by type via shortcut, general lack of direct unit control outside the possess mode - makes battles with other keepers messy since your Imps will move into the frenzy and get killed)

-Sometimes weird AI (powering up a spell targeted at one specific creature causes all creatures on the same tile to stop their actions (same thing happens while slapping or picking up your Imps - slows you down when several of them stop), drop an Imp in front of what you want it to work with and it might do something else instead)

-Inverted up/down view during possession
-Spells 7-10 are invisible in FPS mode
-Can't play as the good guys - answered
-No difficulty options - answered
-Lack of hotkeys for building a certain room/selecting a certain spell

Research is still a predetermined order in DK2.

I don't use many traps, but the spells are generally useful.

It's been a long time since I played DK1, but I think training is faster. An important difference is that the imps level up by working the dungeon - digging rock/gold/gems, claiming tiles, etc., so you don't have to specifically level them in the training room. BIG improvement.

In the Skirmish maps, there are 3 levels where you get hero creatures instead of the evil creatures (the "Frosty's <x>" maps).

There is not a "Difficulty" level per se, at least for Skirmish levels, but you can change the "type" of AI Keeper you play against - "Master Keeper", "Psychotic", "Idiot Keeper", and others. I haven't played with those options ("Master Keeper" is the default and I leave it set to that) so I can't say how they vary in terms of difficulty.

On most maps the Master Keeper is easiest (it tries to build large rooms, so runs out of gold fast) and Idiot is best (it builds small rooms, so it gets a combat pit quickly to attract knights).