diablo-3
In my opinion minimap takes too much space in Diablo 3 upper-right corner. Is there a way to make it smaller?
Optionally – is there a way to make minimap behave like in Diablo 2 when it was constantly semi-visible and overlaying gameplay? Cos when I toggle it fullscreen my character stops responding shortly.
The standard movement speed is as fast as it gets in Diablo 3. There is no run/walk toggle because you're now always running. Stamina no longer exists, and there's no real reason to ever move at a slower pace.
As for running faster, however, there are items that increase your movespeed. You are most likely to find this affix on boots, although it also exists much more rarely on other items.
Here is a partial list of affixes discovered so far and their properties. What you'll be looking for are boots that are Quick or Nimble.
You can change region before logging in. Look into Account tab, inside Options menu.
As you said if you want to change region (this feature is available when all region has launched the game) you have to start a fresh character and you cannot do it "on-the-fly", but you have to exit and re-login.
Best Answer
Right now, there isn't a way for doing either of those things.
Specifically, your second question is answered in more detail here.