Superboy tells Alanna in "Earthlings" that he broke it off, because Miss Martian "left [him] no choice". It was later revealed in "Depths" that he broke up with her because he disapproved of the way she "abused" her psychic powers and because she tried to tamper with his mind.
Why are the Leaguers wanted criminals?
As revealed in "Earthlings", during the 16 hours the six Leaguers were missing, they were sighted in Rimbor, and whatever they did there caused them to be considered wanted criminals, and by extension, every member of the League is unwelcome in the entire sector.
As seen in "Alienated", Aqualad left the Team after blaming them for Tula's death, and discovering that Aquaman kept his true lineage from him. He is currently working with his father. However, in "Depths" it was revealed that this is merely a ruse and he is working undercover for Nightwing to get close to the Light and ascertain the identity of their Partner.
Wally and Artemis have left the Team and moved to Palo Alto where they attend college together, as seen in "Salvage".
In "Bloodlines", Nightwing reports that the Kroloteans were kidnapping humans for study and search for a "Meta-Gene", which, as explained in "Before the Dawn", is genetic human marker that indicates mankind's potential of withstanding catastrophic physical trauma by developing superhuman abilities. Presumably, the Kroloteans wanted to weaponize it, just as the Reach (their competitors) intended to.
In "Before the Dawn", the Reach ambassador explains that it is a genetic human marker that indicates mankind's potential of withstanding catastrophic physical trauma by developing superhuman abilities.
It was revealed in "Intervention" that an ancient ritual had been performed to free the Scarab of Reach control. After Blue's Scarab was put back on mode, Zatanna performed the same ritual to free it again.
It is revealed in "Summit" that Godfrey's initial support was part of the Light's plan to ultimately turn the populace against the Reach. Further, in "Endgame", it is revealed that Godfrey was an associate of Darkseid and an ally of the Light.
What does Vandal Savage mean when he says that the Reach's drink contains everything that they need the body to need?
As stated in "The Fix", the chemicals that make up the additive in Reach would, over generations, addict the human population to the drink.
What is the additive that the Reach is using and what does it do?
As shown in "The Fix", it contains a trace amount of chemicals that would, over generations, remove the will of humans to resist Reach subjugation. It also had a mitochondrial marker that would make it easier to identify, isolate, and locate people with Meta-Genes.
What is the alternative to removing the Scarab that Green Beetle referred to?
As shown in "The Fix", Green Beetle claimed he could use his innate abilities to reach inside the scarab and silence it. This was ultimately a ruse to allow him to reboot and reprogram the scarab.
Was Green Beetle truly sincere in his volunteer "debrief" to Miss Martian?
No. In "Runaways", he was shown to be an agent of the Reach, working with Black Beetle to corrupt Blue Beetle. In "The Hunt", Miss Martian realized that he and his scarab fed her only what they needed her to see.
Did Green Beetle really fix the Scarab to let Blue Beetle have full control with no problems?
No. In "Runaways", he was shown to have secretly reprogrammed Blue Beetle's scarab so that it followed Reach directions and took control of Jaime Reyes.
Arsenal was fighting for his freedom in the Warworld, where he eventually aided the runaways in rescuing the Team. Sphere was sucked off into space, but was reunited with Nightwing and Miss Martian, and helped them locate Superboy. Both events occurred in "The Hunt".