Lockheed was last seen in "Astonishing X-Men" vol. 3 #24 (March, 2008), silently watching Kitty depart Breakworld on a space craft. They never did say goodbye, Kitty did not forgive his affiliation to SWORD.
Yes but you misremembered Sinister's role there. He is actually using his own name "Nathaniel Essex" because that was the man Herbert Edgar Wyndham (High Evolutionary) knew as his mentor. Apparently Herbert had not bothered to check what was his mentor up to for the last decades and did not realize Essex had his own agenda.
Note that while Essex was the teacher and Wyndham the student, Sinister went out of his way to acquire HE's equipment. Apparently the student surpassed the teacher some time ago.
I would think the New Avengers are underpowered for such a conflict. Faiza has complete control over organic matter and has been able to immobilize opponents in mid-combat. Captain Britain's power level currently depends on his own self-confidence. He can presumably increase it enough to beat Cage. The guy has faced the Fury and won. Spitfire's super-speed would allow her to strike Ronin and Echo before they get a chance to react. Black Knight can use the Ebony Blade to cut Wolverine to pieces as the blade cuts through soldid steel with ease. Wisdom could use his hot knives to put an end to Iron Fist and Spider-Man. Blade can presumably realise that he is useless to his team.
White Rabbit is supposed to look silly. She mostly appears in comical adventures after all. In "Spectacular Spider-Man" vol. 2 #185 (February, 1992), she mentioned calling Yellow Claw. He didn't turn her down. He just could not stop laughing.
Long time due. Emma has shown the ability to shape formidable strike forces out of relatively inexperienced or underpowered teams. She has strategic skills as seen while calling the shots for Generation X. She just needs an opportunity to showcase her leadership and utilize the X-Men's resources for maximum benefit.
He has more experience than most other X-Men due to service with the Avengers, Defenders and X-Factor. However the only team he ever attempted to lead were the Defenders and most of them claimed leadership for themselves at the time. The situation was resolved by granting leadership to Candace Southern and letting the level-headed lady call the shots.
Thor has about two thousands years of experience in combat. Previous incarnations of him have been active for far longer but he does not retain their memories. I was under the impression Black Adam has the advantage of experience here.