You don't need one (if I understand you correctly). Your muscles (which are meat) are made of protein (as are a bunch of other bits) which is made up of amino acids. Basic biology 101
I guess there are all kinds of tests you can carry out these days. Probably pretty expensive and most likely not very accurate just like any other food test or whatever.
Not to my knowledge. What exactly are you looking to accomplish? I mean even if you could find out how well your body uses aminos, it's not like you can do anything about it
Not sure what you're asking about. Are you asking about how well your body utilizes ingested amino acids, or your body's own production of amino acids?