Welcome back to the game @Zelebra! Always good to see returning players. :)
Incarnates - In general, I believe farmers and Incarnates will be separate things. I don't do it myself because I find it particularly boring but AE farming is still a thing and most will build a character to maximize gain in the farm since the created mobs will be very specific, doing so would not equal a good Incarnate build as iTrials will have a much wider range of foes to deal with. Other will be able to better speak about this.
Missions - The only way to learn is to go out and do. Skipping content by PL'ing your character is not going to learn you much in the way of forming/leading teams/leagues. Joining other teams, especially regularly run TF's/SF's like Torch's SNS (Saturday Night Synapse) and following (and taking note of) the instructions of the League leader is a good way to learn how to be a good leader yourself.
Leveling - See missions.
Badging - Install VidiotMaps for things like exploration badges and plaques, install popmenus for keeping track of everything badge related. There are threads for both and a dedicated Badging section in the forums.
SG's - Check the server sections in the forums as well as on Discord for SG's offering invites. Personally, I'd recommend teaming with folks first to find a like-minded group of people before just jumping into any SG.
Go. Hunt. Kill Skuls.