Shang Chi vs Hawkeye:
It depends. If its just "normal" Shang-Chi, then I'd say Hawkeye takes it every time. Shang is a much better martial artist than Clint ( /understatement ), but Clint is a ranged specialist with a very large and nasty selection of trick arrows, and Shang doesn't really have a good counter to "impossible marksman shoots me from 100 feet away with something nasty".
If Shang Chi gets the ten rings? That changes things a lot. I'd still say Hawkeye takes it occasionally ( his trick arrows are *really* good, and the Ten Rings don't exactly give passive invulnerability ), but Shang Chi wins at least 8/10 thanks to having much better defensive and ranged options.
( If the fight starts at like five feet, then sure, Shang wins every time either way, but conversely starting it at a two miles away, Hawkeye would win every time even with the rings. I assume starting range and conditions are such as to not be obviously one-sided. )
Black Panther vs the Mandarin:
Black Panther every time, because the Mandarin doesn't exist.
Black Panther vs Wenwu:
I think Wenwu should take this the vast majority of the time. In terms of physicality, they are at best even given the rings, and really Wenwu has a large edge in everything but durability. Wenwu is at least as skilled as T'Challa, probably moreso. Wenwu has numerous powerful ranged attack options. And while the vibranium undies provide a lot of protection, their protection is not infinite, and Wenwu deals out a *lot* more damage than things we've seen effect BP. Its not that this fight is a curbstomp or anything, but T'challa is just in a really bad position. He needs to get a clean shot with the claws on Wenwu at point blank range, and that just isn't going to happen unless Wenwu makes a lot of unforced errors. Its otherwise going to consist of "Black Panther gets slammed, blasted, and electrocuted from varyingly moderate distances repeatedly". Wenwu 9/10, with the one victory being where T'Challa successfully parleys his absorbtion blast into a setup for a decisive melee attack.