All right, I'll take a shot at answering your questions.
First, all the DZ actives in my chapter, or that I ever met, for that matter, were undergrad. I don't believe DZ allows grad students to remain active (correct me if I'm wrong...I'm sure
KillarneyRose would know this, since she knows all things DZ
). However, if you are still an undergrad, I don't see any reason why you wouldn't be eligible for a bid.
Second, if the DZ chapter at your school didn't have a very big pledge class last time, I assume there's a possibility they might take more women than, say, other chapters who had larger classes, if they are under total. (If they are participating in COB, then they are under total.) But here's the thing--they may have more extra spots than other chapters, but that doesn't necessarily mean that they will give out enough bids to fill all of them. COB is usually more relaxed than formal recruitment, but chapters are no less picky.
Third, recs always help! I didn't think this was true, especially since my school states in the rush brochure that recs are NOT required and that individual chapters must secure them if they are needed. However, this is a load of...well, bull. Even if your school doesn't generally make a big deal of recs, I'd get one anyway. You never know. It might make you stand out a little more.
Hope I helped!
Good luck!