I think all the advice you've received so far is good. In terms of visiting them at high school events, I say go for it. I was pretty active in a few clubs at JHS and got to know parents well, so when the students went on to high school they'd usually invite me to their games too. I was friends with the local high schools ALT so we'd go and the parents always seemed happy to see me there and they'd talk with me. A few invited me out for drinks with them, or to their house for dinner. I think it's really dependent on how well you know the parents and how they would interpret social media contact. A few of those parents added me on Line, and then had their kids add me through it too, which I found odd. But if the parents are leading it I'd say you're good. As long as you're not the one seeking it out or initiating conversations I think it's fine, especially if you're account is public. You could always block them from seeing stories on Instagram if you want to share more personal things.