Male teacher told me I'm ugly in front of the class

Sometimes people look ugly to people who are unhappy. Shitty way to express your unhappiness though.

A counselor would pick on me for a style of clothing I liked

Needs more context, sounds like general people-being-odd-about-odd-things or having hang-ups. We all encounter someone at some point who has an issue with our choices and style. Or maybe you really were wearing something unusual, which is fine but when you do, expect some people to get ruffled about it. That's why some people wear unusual style choices, to provoke reactions in people.

Grandfather beat only me out of 20+ grandkids

I've heard more than one story of grandfathers abusing kids who remind them of someone they loved in their life. Or maybe you just got the unlucky dice roll with an asshole. Again, people have shitty ways of addressing their unhappiness. But this is pretty serious, because physical abuse can lead to all kinds of issues later in life, like:

The only boyfriend I've had was severely abusive

While it's not your fault that you were abused, I'm going to hazard a guess and assume that you endured minor abuse from him before it escalated to "severe" abuse. You had some shit happen to you when you were a kid, and this is making you have some self-esteem issues that may make it hard for you to understand danger signs, your place in a relationship, and what you really deserve. It's not your fault but you have the power to recognize where some of your issues might come from, and start working on fixing those issues.

Random guys in public make fun of me

You are either encountering the random douchebags that we all encounter from time to time (I've been made fun, some people are just dicks) or you're projecting some kind of odd personality quirk which might also be related to your abuse history, or you're still wearing that ridiculous outfit that your councilor kept picking on! (Sorry, small joke, but this example is too vague to really address or get any meaningful perspective from.)

Virgin friend who always whined about wanting sex with anyone flat out rejected me when I offered a fwb thing

My experience has taught me that the stereotypical Virgin Whiners are not whining that nobody will have sex with them, they're whining that a particular girl or kind of girl won't have sex with them. Or they're just whining so people try to console them and feel sorry for them, or they're expressing self esteem issues and really aren't ready for a sexual relationship... which is often why they remain virgins well into adulthood.

Old classmate threw and broke some possessions he took right out of my purse

Did most of these things happen in school? Are you still in school? Because school is full of dumb teenagers who haven't learned how not to be dumb teenagers. It's dumb kids that make school hell. Everyone hates school just because of the dumb kids. None of that shit will matter in a few more years when you make adult relationships.

Old after school program leader would purposely ignore me, and I've overheard him laughing to the other leaders about me

Did you confront him? You should confront people that you suspect have a problem with you. You just walk up to them and make eye contact and ask firmly if they have a problem. If they dodge the question you repeat it more firmly. Best case you get an honest answer and can learn from it, worst case they try to laugh it off or make excuses because they're guilty... but I promise they'll learn to keep their damn trap shut after. Try this sometime. I promise it feels AMAZING. If you've never stood up for yourself before this is like goddamn BUNGEE JUMPING your heart will race and you'll feel elated and scared all at once.

I've had several classmates over separate times in my life throw things at my face for no reason, pretty hard.

See above about school. It sucks.

You need to not be abused anymore. You need to get through school and not worry about what other people think of you. Choose good friends and always be ready for people to do the unexpected, because they do. Exercise your body, exercise your confidence by trying new things that make you uncomfortable, and you need to tell someone if anyone ever hurts you, both in the past or going forward. You probably need to talk to someone professionally, and if that professional doesn't help you, you get a different one. Repeat.

Fix all these issues and be ready to dismiss this whole period of your life as "shitty school years" and you'll be fine.