a) There is an old saw mill (wonder what's touristy about it :?) and an island called Jolly Bouy where snorkelling is said to be better than at Havelock. Haven't seen both of them, so can't comment if they are worth the visit.
b) Yes, Havelock is the main tourist destination in Andamans. Make sure you visit Radha Nagar beach in the evening. The other beach (Kala patthar) is not so great, but still good with literally nobody around there.
c) Neil Island isn't as good as Havelock, but still worth a visit. It's quite close to Havelock, so you can take a ferry from there.
d) I stayed in a remote island called Long Island which is one of the least visited islands. It has the most beautiful beach (Lalaji beach) of Andamans, IMO. There is only one resort there (blue planet), which is essentially a group of huts. You can't do camping anywhere in Andaman due to restrictions AFAIK.
e) No idea about trekking, but heard there is a trekking trail from Blue Planet to Lalaji beach which takes two hours.
