I intend to visit the U.k. for tourism this summer. Is it possible that my brother (who is not based in the U.K. nor does he have indefinite leave to stay or British citizenship nor does he live in the U.K. ) sponsors the expenses of my trip? If so, would an affidavit from him, his bank statement and proof of familial ties be sufficient evidence?
Yes. There is no rule that the sponsor as to be a UK resident, citizen, etc. The sponsor has to show that they have sufficient funds to support your trip and that they are willing to do so.
Just think about foreign students in the UK. Many are sponsored by their parents, a large majority of which are not UK residents, citizens - some may even have never visited the UK before!
So there is absolutely nothing wrong with your brother sponsoring your trip.
Evidence would be his financial statements, where he is working (a salary certificate), how much and what is the paying for, and of course his relationship to you.