Choosing research area I am considering pursuing a PhD in computer science one day. 
I guess specializing in (is that the way to put it)?
What I want to focus my research efforts on.
I am interested in:


Manned/unmanned space exploration (writing guidance/navigation systems for the next Mars rover, etc).
Finding cures for diseases (folding @ home).
Computer models of climate change, as I am very much a person that thinks "Global Warming is real and needs to be dealt with yesterday".


But this questions isn't "what should I do research in" but more of "how can I decide what I should do research in."

I know a lot of people will counter with "if you don't know what you want to research then you shouldn't be considering getting a PhD", but I don't believe in that line of reasoning. I want to do research and to be involved with something that expands the boundaries of Computer Sciences as we know it.  Just because I am not exactly sure what avenue I should go down in doing so, doesn't in any way change how much I know that I do want to do it.

So where do I start with figuring out my specialization?
What are my theoretical options?
Where can I see if "getting my PhD to write software to guide probes to Jupiter" is even a viable option?
Must I choose a area that is currently being researched at the university I attend, or am I free to come up with my own?
Can/should I be reading recently released papers on Computer Science topics for some inspiration, and if so where do I go to find those?
This is one of the harder questions you'll have to ponder, and one of the most useful. First off, realize that your choices are not (completely) irrevocable. Many researchers shift areas every 5-7 years or so - the changes are not dramatic, but over time you can make useful contributions in a number of different areas. 

Having said that, what you are looking for is a broad topic that will presumably take you through the 5-6 years of a Ph.D. To look at your questions one by one:


  Where can I see if "getting my PhD to write software to guide probes
  to Jupiter" is even a viable option?


Do you know of people working on this ? maybe at NASA ? Where did they do their Ph.D ? what kinds of topics do they publish in ? What I mean is that one way to figure out if "Ph.D in X" is viable is to see if there are people doing X, and then figure out what their trajectory was by looking at their publications, CV etc


  Must I choose a area that is currently being researched at the
  university I attend, or am I free to come up with my own?


It depends. You're in an MS program, and you haven't mentioned whether you're planning to apply elsewhere for a Ph.D. An MS is a good time to explore your options with people at the university, burnish your research credentials, and build some background in areas of interest. Obviously it helps if your area of interest is covered, but even if it's not, figure out related background that you need, and maybe look for someone doing research in a related area. Also see which places/people you'd like to do a Ph.D at based on the area, and that will give you a sense of what kind of extra reading/prep to do. 


  Can/should I be reading recently released papers on Computer Science
  topics for some inspiration, and if so where do I go to find those?


But of course ! but you should try to focus your search a bit. There's a large body of work in each of the topics you listed, and google is your friend. Once you find even a few papers, you can figure out where they were published, and then look at other papers in those venues, and repeat.