However I don't know the answer.

I am non-union. Am I allowed to audition for union jobs? How does one join AFTRA/SAG in the first place?

Another thing - when trying to get yourself an agent, do you just mass ship out your cover letter/resume/headshot to all the agents near you and hope one bites?

Try using the search feature or even looking down the various topics on the boards for lots of information. Here is one link that I found after about a minute searching:
http://bbs.backstage.com/eve/f.../9131061/m/151109232

Yes. you can audition. There are lots of ways to become SAG or AFTRA -- refer to their websites.

That is one way to find an agent, but honestly, do you think you are ready for that step?