Many people at this age are desperate for answers and guidance in life. Often children get very little attention form their parents, and they spend very little time around older people, who they are supposed to use as models for being the adults that they will soon be. Children are often separated in to age groups with rather narrow age ranges.
I really agree with your trouble with the lying about having a girlfriend when you really don't school policy. First of all it teaches you to lie, and second of all it doesn't really solve anything. From their perspective, even if you did have a girlfriend, couldn't you break up with her, or have two girlfriends?
If you feel up for it, you can answer their questions with short pieces of wisdom and advice that may be valuable to their lives. They look up to you because you're older. Saying that "you have a girlfriend" enforces the idea that everyone must have a boyfriend or girlfriend. That's something that their minds are already full of and you don't need to make it worse. It should be perfectly acceptable to say that you don't have a girlfriend, and that you are spending time with other things in your life at this time. If you want to be a good model to them and you're able to, you can tell them a couple of sentences about girls that you've liked in the past and the nice things that you've done for them. Maybe it'll help them realize that being with 13 year old jerk who thinks he is better than everyone really isn't a path to happiness, and they should be strong and ignore the peer pressure. Be careful to not go too far and get in trouble with the school though! They may not take kindly to discussions about certain topics, even if it's obvious to you that the kids are already discussing things that are way beyond any bad influence you could teach them.
Also, try not to sexualize questions or take them in a bad way if you can. If somebody says "You look sexy", you can say "Oh so you think I look like a man? Thanks". It's not really a bad thing to be dressed up and look like a man after all, since that's what you are. Try to direct their thoughts to good things.
Again, I'm just talking about short phrases here that are good truthful answers. Not you becoming their relationship counselor. You can just ignore them and tell them to get back to school things once their questions become to silly and pointless.