"One thing though there is this wire that goes from the alternator to this round thing that screws into the block that was a little loose what is that?"

This sounds like the alternator ground wire. Usually some sort of blue, about 10 gauge, red sleeve on one end that is a marker and strain relief but normally hides the utter failure of the crimp connection underneath. n When it fails (normally intermittently) the charge light will flicker (or not) and you will chase brush kits, new alternators and all sorts of things as the source of the problem when all along it is stupid little wire.

"I did hook up the battery to the charger and it shows a full charge immediately. "

This does not rule out a bad battery (though it is pretty good indication) as our race car recently had a battery that show 12.5 volts about 2 seconds after hooking up the charger but withing 30 seconds it was reading 8.6 volts with it disconnected. Click the starter and it dropped to about 4 volts and obviously did not do much.

If this is an automatic, I am starting to think neutral safety switch.

That said, the rebuilt starters have gotten very bad reputation of late including that that are supposed to be genuine Bosch.