In my experience BA treat people very well at interview. They are courteous, professional, and fair to all. You can get a job regardless of whether you have a mate in the company, unlike some.
It is their right to ask whatever questions they like at interview, and if you struggle to answer them I suggest you aren't what they are looking for - no reflection on you as a person, just not what they want.
SQ and CX need expats to crew their a/c, hence they are willing to fly in people from all over the world. BA have a huge pool of willing applicants on their doorstep, hence no need to pay people to travel to them - simple economics.
As to basing your career on whether or not you have to buy a sandwich at interview, it is slightly short sighted. There are many pros and cons to BA, but having to lay out £1.95 for lunch doesn't feature highly on most lists
If you are a direct entry jet pilot, surely you can use staff travel to get to LHR for peanuts. By not atending the interview I think you are cutting off your nose for the sake of a few quid and your ego.
P.S. I wonder if you will reconsider if CX and SQ say no!!!!