Nope; if you’re not a Hindu, you have no caste, and are (to a strictly orthodox person) lower than the lowest caste. There are apocryphal stories about Hindus helping wounded English men and women during the 1857 mutiny and being rejected by their families afterwards. I’m not sure if these stories are true or not, but I would say that I’ve met some really orthodox Hindus in my time (my grandmother was one of them) and they can be very strict about this.
ETA: I think the term you’re looking for is “Kshatriya”.
It depends. For women, definitely no walking about in underwear. Men get away with a lot more, at home. I wouldn’t, but then again that’s a personal thing. Although my family’s very liberal in general terms, nudity at home is a cultural taboo that remains.
ETA: Re: bathroom habits, personally it’s a case of when in Rome, wipe as the Romans do. I do think water is cleaner (at least I feel cleaner) and a good scrubbing with soap and water (twice) is a must. Also, if you don’t scratch with your fingernails, the problem of contamination is much reduced.