While- not really a grammatical question, but worth a few remarks. The Harbrace College Handbook, by editors of Harcourt Brace Jovanovitch, publishers, cautions "Do not overuse [while] as a substitute for 'and' or 'but'. The conjunction 'while' usually refers to time."
No mention of whilst, but I had an English co-worker who said that he was taught to use it in school. When I was editing papers for a journal, I changed it to while, but the journal was American. I don't know if it would be acceptable to an English editor, but I suspect some publications would accept it and some not.

Many handbooks on 'style' and usage. For North America, the Chicago handbook is most followed.
There has been much discussion in previous threads.