At high temp, radical will form so make free radical intermediate and check stability. Note that radical will form at double bond, not at allylic because allylic happens when sunlight is given or with nbs..
Racemic mix will form because there is formation of a single chiral carbon bro. The first carbon that you have star marked is not chiral. Two same methyl groups are there.
b)yes with nanh2 E2 will happen but don't forget that both in E1 and E2 saytzeff is major as in E2 there is double bond character in the intermediate
c) ans given in above pic. With bulky base, hofman dominates
Why are u saying carbocation will not rearrange? It will. What is the ans given in 11
Ask if any doubts @pratyaksh_tyagi