pepsico

I'm international and I don't have any publications, so I don't think you should worry to much about publications. I would think, in regards to your research, the LORs are what matters. If they describe your work in an attractive way, and they are deemed trustworthy, I doubt a publication makes much of a difference. I think all adcoms will be aware that if an undergrad publishes or not is very much a factor of what kind of projects they get, rather than their own input. 

I agree with the above advice. However, I will add that you should also apply to some safety schools if you're determined to get into a program. All the programs you have in your signature are top programs that are difficult to get into even with excellent letters.

I think a GRE retake would have a minimal effect on your applications. Your scores are pretty good. You can reevaluate your SOP and letter writers. Additional experience, academic or industry, will help. Keep in mind there is still a month or so before most schools give out the bulk of their acceptances.