HI Jouda and welcome to the forum!
Regarding it's bald butt

This is a common occurrence amongst new world tarantula's with urticating hairs. These are the hair that they, when they feel threatened, kick off t in defense. The bald spot should be gone after the next moult.
On your second question: some members may disagree with me, I usually upon arrival look to see if the tarantula looks well fed or not. I have had some T's who took prey on the first day, some after a few days. My best advice on this would be to put in a prey item, and leave it for a while to see if it takes it. If not, remove the prey and wait a bit. (Do this over night, as T's venture outside more often during night time.)
And on your third question, I have a few T's that webs like that, but they do have means of getting out, believe me.
I do have a Brachypelma Albiceps (Golden red rump) of about the same size, and the only time mine webs like that is just before it's going to moult (pre-moult). It spends most of its time out in the open in other regards.