A:AnswerNo it doesn't it runs 95% of everything out of the chrome browser. You can either do the chrome browser app and extensions or some chrome OS apps.
A:AnswerIs your tablet an android? There is an app called airdroid that I am going to try with my Samsung android phone. I haven't yet. You could also transfer files by putting them on Google drive and then you could access them from anywhere.
A:AnswerYes. The HP 4501 printer allows users to email any document to it by using eprint. It should have come with its own email address. In addition you should be able to set up cloud print to print to it. I have an HP 5510 and since I had already set up cloud print to print from my android phone, my chromebook recognized it and I can print that way or with the eprint email address for my printer.