Good on ya! You're learning the "hard way", discovering everything for the first time, and enjoying it.
Terminology (especially when you sail solo so no crew to understand what you meant) is secondary to learning physically what to do. So don't sweat it, the vocab. will come in time. Even so..
Your first
line? A halyard (old days, "haul yard", I'd guess)
Your second
line? A sheet, or mainsheet in this case since it's the "main" (and only) sail
Those "pulleys"? They're blocks
"Pulleys that redirect the
line"? Easy, they're turning blocks
The rudder hangs on the stern, connected to it is the tiller. Sounds like one of the mainsheet blocks clips on to the top of the rudder.
You're right, switching sides upwind is tacking. That series of tacks you did is called a "beat", or "beating upwind"
Now you can sound salty at the bar. But correct terminology or no, the main thing is you're learning (on a small boat, which I think is the best way to start) and enjoying it.
Your problem in getting stuck upwind in mid-tack is common in light air. Try starting the tack at max speed and turning faster, and you'll probably make it. If you get stuck again, try sculling (pumping) the rudder hard over, which may help. Or, if you want to get fancy, push the boom out towards the side it used to be on, with the tiller the opposite way, and you'll "back up" like backing a car out of a driveway, onto the new tack.
So keep on, and keep on asking questions.