Anon, this won't simply be favouritism by teachers. And there are other ways to handle this, without blaming the school or children.
The photo thing may be simply because the children were in a group with the adult who had the camera. Have you ever helped on a trip? The teachers are so worried about risk assessments, counting heads etc, making sure everyone is in a photo is not always going to happen.
I was on a sports trip last year. My ds2 won the event, but he's not in many photos - he was very much cheered on and encouraged during the day, but simply wasn't near the teacher who had a quiet 5 mins with a camera.
As for the other stuff, I'm afraid it sounds like jealously and insecurity. If you really want to make your child more visible, then you can. It's not just a question of making friends with the teachers, it's showing your children how to grab opportunities, and network.
If your child wants to make the sports teams, they have to put the effort into the sport. Turn up to practice, even in the rain. Don't give up if they are not picked at first. Encourage their team mates on. Sane with school plays - if they're that bothered, get your child yo a local drama group. Let school know it's their "thing".
And, as for charisma, you certainly can't ask a child to turn it off. My ds1 has no idea, he is completely oblivious to it, but he's been the same since he was four months old.