The wasd controls not working as expected can be caused by having multiple keyboard layouts installed and swapping between them by accident. Try hitting win key+space or left alt+shift to change between keyboard layouts. If that doesn't help try typing wasd in chat to see if the keys are at least mapped correctly to the keyboard.
Right click making you run forward shouldn't be caused by this though it could be caused by switching windows (alt+tab) while the left mouse button is pressed, the game doesn't always pick up on key press changes when that happens.