To clear things up, here is some background information for the timeline of Full Justice.
Robin of the Teen Titans in this universe is not Dick Grayson, and is instead Dylan Grayson who is a distant relative of his. While he has no current plans to be featured in the story as of yet, it is likely he will, or at least have frequent references.
Beast Boy of the Titans is a different hero from the Young Justice version, although they are in the same universe as each other and go by the same name. While this Beast Boy will appear, he will likely be referred to as BB2 or something of that likeness.
Kid Flash from the Titans universe is also a different hero from Wally West going by the name of Kid Flash. Plans for him to appear are still very unknown and unlikely.
Bart Allen is now no longer Kid Flash II, and now goes by Impulse again, for reasons to be revealed later although the IRL reasons being I personally prefer Impulse's original identity and it causes less confusion of him with Wally West.
Artemis is still using her Tigress identity and is still dealing with a lot of emotional stress from Wally's death. Following her conversation with Impulse in 'Endgame', the two became close friends and rely on each other when in need.
Static left the Team to join a new group of superheroes who are stationed in a foreign country.
Jinx, who reformed towards the end of the Teen Titans canon series thanks to Kid Flash, still remains a hero and has been heavily affiliated with the Titans ever since. She no longer is dating Kid Flash, and has recently started a relationship with Cyborg (a reference to their romance in the episode 'Deception', along with their further explored relationship in the spin-off Teen Titans Go!). She will appear along with her boyfriend, and will have some plot lines.
Terra is confirmed to be alive. Her history and story will be explored and explained from what happened post-Aftershock.
Raven, Starfire, and Cyborg have recently left the Titans and have began to travel together and fight villains along the way. Robin and Beast Boy remain in Jump City, where three new super heroes have joined the Titans in their place.
The Team, although initially working side-by-side with the Justice League and sharing the Watchtower, decided to break off and be slightly more independent. While they are still just as affiliated with the League as they were before, they are in charge of running their own missions and assigning tasks, though they occasionally receive an instructor. The have rebased back in the Warehouse and eventually found a way to restore Mount Justice to its prime.
Robin and Wonder Girl are still dating, although their relationship dynamics aren't always the best.
Lagoon Boy has become aware of his stubbornness and attitude and how it has affected the others. He's trying to work on improving, although frequent slip-ups occur and our followed by many apologies.
Nightwing is still on leave after Wally's death, which has had the heaviest and darkest impact on him.
The Ben 10 universe will eventually combine with this one, although those characters and plots, while prominent, are considered more of B-sides to the story, so it is not an official crossover with Ben 10, but can definitely be considered that.
The rest of the characters' current statuses and background information on the timeline since the last episodes of their respective series will be revealed and discovered as the series go on.
So now, get ready to enjoy Full Justice (coming soon)!