How to reset the movement speed, after messing around in the console

You can change your base speed using the console, which you can open using the ~ key (or whatever key is to the left of the number strip at the top of your keyboard).

Type player.setav speedmult x where x is the number you want for your walking speed; the default is 100.

You can either increase or decrease this number. Increasing it higher will result in super fast running which man ruin the reality of the game.

I'd recommend player.setav speedmult 125.

In my opinion the default running is way too fast, and the default walking is too slow. While holding Alt to sprint is perfect. The only other way I know to edit these values is to open the core files, like XML with a text editor, but I won't go into that much detail here. You should be able to Google it.

There doesn't seem to be one. However, since you're using the console anyway, you could reproduce training with advskill to level up the skill and then remove the proper amount of gold from your character with removeitem.

player.advskill <skill> <nn>
player.removeitem f <price>

This article has the formula for how much gold it costs per level and this article explains advskill in detail.