Your bags should get checked through. I have only flown American internationally and it was just like any other flight through Terminal A. I would verify with your airline. Have fun.
No your bags will be checked to your final destination.
I'm betting (from my old travels), your luggage will be there waiting when you arrive. Be well and safe travels 👍
As long as your original flight originated in the USA, the answer to your question is no, you do not have to collect your bags and go through security.
Your already inside the airport from an arriving flight, all you will do is get to your next gate for your next departure. Everything is checked through to your next connecting flight. Safe travels, enjoy London!!+
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