I'd like my skills to progress by hitting or casting spells on training dummies. Is this possible at all?

Almost certainly it can be modded for the PC version once the CK is released.
But honestly, it's not too hard to level your combat and magic skills by actually killing things.

Yeah, that's true. I guess I just want it for roleplay reasons. I wouldn't even mind if the gain is slower than fighting actual enemies, but the main problem is this, that if you focus on non-combat abilities you will still gain level, which means enemies are harder than you are, so this would give you a chance to level up your combat abilities without the risk of constant death. Well, hopefully the CK will be out soon and the mods will stream in.

I think they should only level you up to a certain point. There's only so much you can learn by swinging a sword at a non-moving target. Maybe up to 30 or 40?