These are very basic things in Mathematica. If you are having problems with these, my guess is that you are new to it? If so, you should go to the help menu >> Welcome screen >> Learn with guided examples. (the welcome screen is there on my student version at home, but I think I've seen it on others too.)
That guide is a first introduction to Mathematica, shows you how to enter expressions etc. I think it actually explicitly goes through what you need for each of the problems you listed.
After you've done that, the next step would be the documentation center. You can bring it up by pressing F1. There you can surf the documentation of the mathematica language. Stuff to search on for your problems would be maybe "equation solving", "integration", "differentiation" and more. the exampled how to use functions can be very helpfull.