The misdemeanor convictions likely won't hurt your career, but depending on the nature of the felony you might have a hard time. For example, I've seen a felon with a computer fraud and abuse conviction get all kinds of great job offers. Conversely, at my company we tried to hire someone who had been convicted of murder and served his time, figuring he'd paid his debt to society and that this was now irrelevant, but our hiring decision was overruled by the legal department. Finally, there may be specific felony convictions that prohibit certain job functions. E.g., if you've been convicted of any kind of embezzlement, you may be barred from jobs that involve managing government grants. Sex crimes obviously carry a huge stigma. And though the drug laws are a bit out of control, I'm not sure how bad drug convictions, at least if you aren't working with kids. My company is required by federal law to be a "drug free workplace," which forces us to sign documents, but the content of those documents isn't as restrictive as you might think--basically we have to agree not to use, possess, or distribute drugs at/during work, but what we do on our own time off company property is our own business. A past drug conviction wouldn't be a problem.

Well, Scott Aaronson has written: "If Vinay Deolalikar is awarded the $1,000,000 Clay Millennium Prize for his proof of PNP, then I, Scott Aaronson, will personally supplement his prize by the amount of $200,000.

"I’m dead serious—and I can afford it about as well as you’d think I can." See his blog.

Well, I'm a professor at a research university, where most Ph.D. students are RAs (except while they TA or have outside fellowships). Several of my Ph.D. students have gone on to be professors at top-ranked universities, so I'm probably at least an okay advisor. So let me tell you that advising Ph.D. students is all about respecting them and their ideas and opinions. It's also about trying to instill good taste and values in students. I am shocked to see someone who claims to be professor have so much contempt for his or her students.

As for licensing software, I always explain to my students that they should make their projects free software to have the most impact. I discuss the options with my students, but generally let the lead student on a project select the particular license, ideally with rough consensus of all involved. So yes, even though the university might own their work, my students are free to continue using it and building on it in perpetuity.

It would be wrong for me to confiscate students' intellectual property--particularly if I tried to make them sign something saying their work belonged to me, as opposed to the university. Moreover, it would be setting a terrible example and instilling bad values in students. Finally, it would probably be illegal, because the university has policies in place to prevent the abuse of students.

Yes they can take away all your rights to the software, but no you shouldn't allow them to do it.

First, I've been a grad student at one university and a professor at another, and I've always avoided signing these agreements. It turns out that if you just avoid signing them and aren't too confrontational about it, you can easily slip through the cracks.

Second, you should talk to your professors and see if they will allow you to develop software publicly under some irrevocable license like the GPL or BSD. With revision control software like git, it's pretty easy just to throw the repository on your home page and make everything you do available to the world (including yourself) on a royalty-free basis. Import some GPL-ed third-party code into your project for extra protection.

Finally, sometimes professors do try to exploit grad students for the purposes of launching their startup companies, etc. If you feel that you are going to be in a position where your research is compromised (for instance because your results are no longer reproducible by the community), then you should find another research group to work with!