Generally, you can turn around and thrust a little bit to hold yourself steady and stop the forward momentum. I had thought about adding a stabiliser, but never actually implemented it.
As for the mouse-aiming: I find mouse movement very, very awkward and I just... don't like it. I started the game on a laptop with a touchpad, so when I started designing the movement and all, it was with keyboard-only in mind. I finished it at a desk with a traditional mouse, but it never occurred to me to include mouse-aiming. If I ever return to it, I'll add that as a setting.
Plus, not using a mouse for anything but menus makes it super accessible. I cannot play a lot of games that require agile use of a mouse and wish they had a keyboard option!