A:AnswerYes, it should work fine.
It is a standard USB keyboard. I have tested it on a 10 year old Windows 7 Dell computer and currently using it on a HP Elite 6th gen Intel i5 Win 10 computer.
A:AnswerIt should work fine. These should be recognized as two different devices. You should not need to buy a different mouse. I have not tried this particular combination you have described personally, but have had both a wireless mouse and a wired keyboard in the past work without issue.