Is it possible to connect two mice and two keyboards to the same computer to be used by two people at the same time with separate monitors?
The first part of your question is possible. There are several utility programs that allow you to implement two mice/keyboards on your PC. I suggest using a Keyboard/Video/Mouse KVM, with this implementation, you can not only connect multiple mice and keyboards, but multiple monitors.
Now, the second part of your question where you want to do this simultaneously, well, that is not possible. Only one keyboard or mouse can be used at a time and when you need to use another one, it will deactivate the one that was active.