I have two sons aged 13 and 15. I think one of the biggest challenges of parenting today is keeping children safe online and where to draw the line with screen time/social media/internet access and so on.
There are no right answers - you have to know your children, establish trust with them and establish your own boundaries. We are told constantly by our children that we are the ONLY parents who don't allow phones in bedrooms, the ONLY parents who don't allow their children to play PS4 for 6 hours a day, the ONLY parents who don't bring children their tea IN FRONT OF THE PS4 (FFS) and the ONLY parents who don't allow their children to Snapchat all night long. Oh, and the ONLY parents who respectfully and repeatedly suggest/insist that phones are put in another room while homework is being done. I don't care. Firstly, I'm sure this isn't true, and secondly, as with almost every other aspect of parenting, other parents can do as they please. They can feed their children rubbish, they can buy them awful clothes, they can value or not value education, team sports, music, art, drama, dance, or anything else. That's up to them. In this area, as in all the others, YOU have to decide what YOU believe is right for YOUR child/ren, and then communicate that to them and stick to your boundaries. There could well be many times when your children will tell you that you are unfair or too strict, but it's YOUR house, they are YOUR responsibility and it is up to YOU to set the rules.
In our house, we monitored phone access sporadically for the first year or so, but haven't done since. We once had to speak to DS1 about inappropriate texting. Phones are not allowed upstairs, ever, for any reason and nor are ipads. We have always stuck to this and it has become a rule that the boys wouldn't even think to question now. 15 yo DS has recently got a computer in his room but doesn't use it as the one downstairs is better. He once got out of bed and turned it on at night - we told him that if he did that again, he would no longer be allowed the computer in his room. He hasn't done it since. If the boys used their phones inappropriately, we would stop paying for them - we have never spelt this out, but I think they know this. They do take the p*ss out of me for telling them that use of screens in the evening is linked to poor sleep (and to be fair, I can't remember where I read that and am unable to back it up scientifically), but they are definitely aware that our rules are made for their sake and not for ours - since, frankly, the rules are a pain in my backside and life would be a lot easier if I just let them do whatever they wanted and sank into the sofa each evening with a bottle of red wine.
Maybe we seem like monstrous parents at times, but we are doing all we can to raise happy, well-adjusted, sociable, responsible, well-educated and interesting people. We will all get it wrong sometimes but what I'm trying to say is - set your rules and stick to them.
For 13 year old children, I think it is appropriate for them to have one account each for their social media outlets (Facebook, Instagram, KIK, Snapchat, whatever) and for you to be one of their friends/followers/whatever. If you don't already, then you could sign up to these things yourself, befriend your daughter and use it as another way to communicate with her. Just don't ever, ever post anything embarrassing on there. I also think it is totally appropriate for you to know her pass code and to insist that the phone/tablet/whatever is always left downstairs when she goes to bed. I think it is appropriate to check her activity on there, not every day but occasionally, and to challenge her about anything inappropriate, explaining why it's inappropriate and why you don't want it to continue. If after a number of challenges, the inappropriate behaviour continues then you could stop paying for her to have access to these things until you consider her mature enough to try again.
If your daughter is joining LGBT groups online and seems isolated at school then that would be my bigger concern. She might need support as she comes to terms with her sexuality, and so might you, if it's not an area you're familiar with. Try to talk to her openly about it, and suggest that you could join online forums together so that you can support her as she grows up, finds out about herself and makes choices. She might feel that she has no friends at school who would understand, leading her to seek 'friends' online. If you are understanding and supportive at home that could make a difference. And definitely speak with her Head of Year or Form Tutor at school to tell them your concerns. Many secondary schools now have LGBT groups and at the very least those school staff should know that you're worried she is isolated at school, so that they can keep a close eye on her friendships and emotional wellbeing.
Best of luck with it all.