The sex is hard to tell, the regurgitating issue could very well be part of the courtship.
Here's a site, hopefully this will help you determine the sex of each bird.
Introduction to Lovebirds
Some good reading if anything.
Its not a must to do what I recommend, I am simply trying to help.
If your little one continues to try and pick something out of his/her beak and continues to rub his/her beak as if trying to clean it, there maybe something lodged into the upper beak cavity that the bird can't get out on his/her own, this may require you to help.
I understand the "mean" issue, we have a few birds here that are set in there ways, this will be "common" when bringing an orphan into your home, a person simply doesn't know about the previous owner (some birds have had many) and how they have raised there bird.
Changing such behavior can be challenging.
From what you have described, this tells me something is bothering the little one, something maybe stuck in his/her beak, if this behavior has stopped, then it could be the bird has worked it out and all is fine.
Here's another link that may help you with courtship.
The Pet Bird Lovebird FAQ
You could have two males, or two females, or one of each.
You will find some interesting reading concerning homosexual behavior.
Regurgitating is fine if it is done during courtship and feeding the young, if the bird does this for the human then this is not okay and or healthy, if this is being done for another bird of the same sex, then this could also prove to be unhealthy.
The more you learn, the more you can stay on top of issues.
I appreciate all you are doing for those birds Jenn, You and your mate are doing a fine job.
Keep up the good work and you will prevail.
Peace
Arty