I learned Mandarin in school when I was a kid before immigrating to the United States, I wanna answer this question, but confused on what you are actually asking about.

But there are some examples I can think of on top of my head (which were learned later on, not in school):

中国共产党 = Communist Party of China

Which shortens to:

中共 which in English would be “CPC”/“CCP”

中 is from 中国 (China), and 共 is from 共产党 (Communist Party)

中华民国国军 (Republic of China Military) --> 国军 (National Army) which refers to the military controlled by the Kuomingtang

In Taiwan:

民主进步党** --> 民进党 (Democratic Progressive Party --> DPP)

I’m unaware of any “you --> u” short hands.

In my household when the minute hand is pointing at 3 (15 minutes), its referred to as 三个字, 字 meaning character.

So for example, if its 12 PM and you have an appointment at 1 PM, and travel takes half an hour, then my parents would say to leave by “五个字” (“Five Characters” aka: when the minute hand points at 5 on the clock, which is 25 minutes)

So basically instead of telling to leave by 十二点二十五分 (7 sylables), its 五个字 (3 sylables)

I’m not sure if this is universal or just my household being different.

I think many Chinese people don’t type text, usually my parents and the older generation aren’t good with typing pinyin and just leave voice messages (on Wechat). Idk what the younger generation does, since many of the younger Chinese people I’ve ever spoken to are Chinese Americans who grew up here.