I'd lean i7-14700K.
Marginally more efficient, a little less total power draw in games (~ 131W vs 143W) and apps (155W vs 169W): https://www.techpowerup.com/review/intel-core-i7-14700k/22.html
and you get the APO features.
Either one will be fine though. 13900K is a little faster in applications overall, but 14700K is a little easier to cool and cheaper to boot.
Not really - they’ll throttle if they run too hot. No need to artificially power limit. They’re engineered that way.
There are also plenty of air coolers than can handle 200-250W