Pronunciation of UI
I've heard "user interface" used quite a lot, but never "yooey" - I'd say the latter was nonstandard.
Personally I'd pronounce it "yoo eye" in technical circles, and "user interface" in less technical circles.
UI is pronounced as "you I"
I work in IT industry and have never came across a different pronunciation.
Youey is informal, and is acceptable for relaxed chat or friends[1]. But for a technical audience you should probably stick to expanding to User Interface for the first use and 'You Eye'[2] afterwards.
This helps people who are not technical (who may not have come across the term before) and also people who don't speak English as a first language, where the initials U and I may have very different pronunciation. ('Uh ee'?)
[1] I do this all the time, and my friends find it endearing, or annoying, I'm never sure which. I also say 'wee-fee" for WIFI. [2] Sorry for not using ASCII IPA.