To determine the gender of the new bunny, you can examine your female’s genitals and see how this new bunny compares. You can also find pictures and illustrations online showing rabbit genitals.
A rabbit of any age can have timothy hay or any of the grass hays. You could also feed alfalfa hay to the new bunny, but that’s not necessary. I assume that the bunny will be eating alfalfa based pellets. You should wait until 12 weeks of age to introduce veggies, and do so slowly. Start with one and feed that the first week, then add a second veggie the next week, and so on.
You can have a male neutered when its testicles have descended. That could be as early as 3 months. Some vets prefer to wait until a rabbit is a little older even if the testicles have descended. Females are usually spayed when the reach 5 or 6 months of age.
You definitely need to wait until the new bunny is spayed or neutered before attempting bonding. That is always the first step. And you need to wait about a month after the surgery to begin bonding. It is usually easier to bond a spayed female to a neutered male, but you can bond same sex rabbits. Try to do the bonding in a neutral room or space. Or you can get an x-pen and set it up in any room, even if it’s a room your bunnies have been in before, because the x-pen will still be neutral to them. I have used an x-pen and found it very helpful, since I can be in there with them and break up any fighting.
Here are 2 good articles on bonding:
http://rabbit.org/faq-bonding-multiple-rabbits/
https://binkybunny.com/BUNNYINFO/tabid/53/CategoryID/9/PID/940/Default.aspx