SRAM - Hollowtech II BB with reducer cap.

I recently bought a SRAM RED22 chainset. I also treated myself to a cheap full ceramic BSA BB to go with it. When it came a noticed it appeared to be a Shimano spec BB with some kind of 'reducer cap' for the left 22mm crank.

I was set to fit this but have now decided to buy a new road frame that will come with an italian thread BB - so intended to fit the SRAM to that instead.

Italian thread GXP BB's come in 2 kinds... cheap and heavy or expensive and slightly lighter but still quite heavy.

I can get a Shimano 9000 Italian BB for less than 30 quid.

3 questions.

Will the Shimano  IT BB with the reducer cap work?

How can I minimise any axle play if it exists? (wave washer?)

Does the reducer cap fit from the inside or the outside? I can't see that it makes that much difference either way. Until I get the frame (and BB) I have no way of knowing how much BB stub will protude. It will come with a low spec Shimano BB which will at least let me test it before laying out more money for a decent BB - but wanted to know in advance is all. 

Cheers all.