First, congrats on choosing UGA!
I am going to try to answer the questions that haven't been answered below... sorry if I end up repeating any info.
How can I possible get 3 or 4 for every sorority? 3 or 4 would be considered a lot. I would shoot for 2... but getting 1 is the important thing. The above suggestions about contacting your local panhellenic and asking teachers are a good idea.
If you don't have recommendations are you automatically cut? That would be considered private membership selection information, so no one on here will be able to tell you for sure. What I can say from my experience is that I was cut by every house for which I did not have a rec after round 1... however, that doesn't mean I was cut for not having recs; it could have been something else entirely! The best idea is to get recs for as many houses as you can.
But with over 1000 plus girls ( this has been on several threads) rushing how do the sisters really get a chance to know you with only a few minutes at each party? It's just as tough as having to rank the chapters after only a few minutes at each party. Just like it's hard sometimes to remember all 17 houses at the end of the round, it's hard to remember all 1000 PNMs. The houses all have their own special ways of breaking things down so it's easier to meet/get to know/remember every girl as much as possible.
Also, several threads have said dress one step up from what is expected. Does that mean a dress and heels, I heard there is a ton of walking, should you carry your heels for the parties and wear something else before you get to each? I totally wished that I had carried heels and changed when I rushed, so I recommend that! Cute sandals are also a good idea... Vera Bradley sells the cutest flip-flops that are really comfy and also stylish.
I hope that helps some!