Highlander is more about teamplay, 6v6 is more about skills, so I prefer HL because it's more relaxed and nowhere as near competitive as 6s. Plus, you can play Pyro there.
In 5cp, koth, payload offense just stick with the medic all the time (along with the demo and the heavy and in some cases the soldier if he's running buff banner for support not roaming with the shotgun), only leave him when someone calls out the spy's location and there are other people to protect the medic while you're gone. Spy is one of the classes which are played on a much higher level even on lobbies compared to pubs, know the trickstabs and don't fall for them, and don't be complacent just because you're a pyro. Also, know when you should just leave them to escape instead of chasing them down. On payload defense stay around the sentry with the medic all the time, don't leave even if the sniper calls out the spy. Use airblast to get rid of stickies and rockets, also be aware that you'll be countercharged when they push in so you can M2 them out of range.
Pyro is classified as an offensive class on the main screen (while demo is a defensive one), that's not the case at all : )