Hooray for a first time trip!
I can’t answer all of your questions, but here’s what I can tell you.
I have never done the shuttle, as I was led to believe it was only available if you book a package through Universal, which I have never done. Uber/Lyft is not an option for me, either, as I, like you, find it creepy. Cabs are one way to go, but if you want everyone in one car, you could use Mears Transportation. I use them when I go and I like that they are waiting for me by baggage claim, we meet up with them and go right to the car and are on our way. It is the most time-efficient thing I have found and I always want to get my vacation started right away and not have to wait on anyone.
In my experience, you will not need the booster seat.
For CBBR, I’m not really sure, but “room requests” at Universal seem to be sketchy at best.
I do not believe you can combine the AP discount with “stay more, save more”. I believe it is one or the other.
Any other questions, just ask. Happy planning!