All new entrants start as 2 stripers, regardless of what you've flown before. How the cabin crew treat you is entirely up to you. Unlike many other airlines, there is no pay-rise associated with 3 stripes. You get your third stripe when you've completed your 4th year. It's a non-event.
In the previous round of recruitment some type-rated DEPs (to 320, 737 and 7576) were given 'short courses'. I don't believe this is something BA had done before. Perhaps this time they're looking at only recruiting rated guys to save costs. This is a shame and it must suck for anyone who doesn't meet the requirements but unfortunately it makes financial sense. I can't see the restriction lasting forever.
You won't get any rock solid details of entry requirements until the day BA publish them on their website. In the meantime, the info regarding type-rating requirements and numbers to be recruited is coming from pilot recruiters. These are line pilots who conduct interviews during periods of recruitment. Some of them have had week long blocks of their rosters cleared for interviewing and have been briefed on some of the details. As I say, that's as reliable as it gets until the day online applications open.
Regarding base choice, I'd imagine that as long as the type-rated requirement stands then your base choice has been made for you.