For the first, Rosen's "Discrete Math and Its Applications" is quite thorough including many solved & unsolved problems.
There are too many good resources for probability & number theory to choose from, so I'd recommend something like MIT OCW for the first one, at least.
The prerequisites are (self-reported) minimum, just calculus and mathematical maturity should be sufficient. I would check it out (it's free) and see if it's at an appropriate level.
Unfortunately I've yet to come across an introductory text or course on probability that is actually good :-(
https://ocw.mit.edu/courses/mathematics/18-05-introduction-t...
I thought there were video lectures available but apparently I was wrong however the class notes are (hopefully!) sufficient.