Playing with the keyboard/mouse combo, you only have two options : walk, or run. No speed increments that I know of. You can crouch to run a little slower or walk at a turtle's pace if you want though.
All keys can be remapped as far as I can tell.
Aiming in 3rd person is actually pretty clumsy even with a mouse, mostly because it's difficult to judge where you character is really shooting, and if you have a clear line of sight. You have to imagine a line between your gun and the target, and must *not* trust the red indicator or you'll waste most of your ammo on the pillar/wall behind which you took cover. It also makes shooting close melee opponents much more difficult, as you can't tell if you're shooting the guy or the wall behind him. Seeing how hard it is just hitting your target, forget about aiming for the head or other fancy stuff while engaged in melee in 3rd person.
If I were you, I'd stick with the 1st person view for combats and save 3rd person for V.A.T.S. shots or walking around. Thankfully, you can switch between each view with a press of a single key (default key is F if I remember right).