Hi Andy, welcome! Sounds like you are off to a great start!
Understanding the chord names does require some music theory, which is covered in more detail as you progress through the GT lessons. The focus on the earliest lessons is just to get you playing, because, well -- that's why you're here!
But, what makes the simple E major an "E" is that the E chord consists of the notes "E", "G#", and "B". First finger on 1st fret of the G string is your G#, and then you have open B string and open E string to make up the other two notes.
There are a whole bunch of folks here who have joined with the idea of learning during the lockdown so you're in good company. I would just caution you to have realistic expectations about how long this will take and how rapidly you will be able to learn. Everyone describes it as a journey and there is no real destination! So try to enjoy the journey and don't put too much pressure on yourself.
On the strumming, it sounds like you probably have a lot of tension in your strumming hand and wrist and arm. That's normal at this point. You want to try to have a nice relaxed wrist. Most of the strum is with your wrist, but a little movement in the elbow too.
Hitting the wrong strings or missing the strings entirely? Yep. That's going to keep happening to you for a long time, but gradually it will happen less and less.
It takes as long as it takes unless you quit - then it takes forever and you will never get there.
