The weapons are balanced and the spawn probability is also balanced. More powerful weapons spawn less often. Pistol and shotgun spawn the most. And they are less powerful because it does not make sense to overpower every weapon ;)
There is actually an acceleration to the character, but it is only present when starting to move or stop to move. If you run, you will keep the speed as long as you run. This is what felt the best during testing. But it is already noted to have a look at in the future.