Yes that motherboard will work with the core i7 7700K, you wont be able to overclock it. And as
WildCard999 mention, you will need to buy an aftermarket cooler (something like Hyper 212 EVO, Gammaxx 400 or the likes, will do the trick).
And no, as long as your mobo is in good condition and you have a decent PSU (Power Supply) from a known brand, the 7700K should work just fine (make sure you have the right BIOS installed on your motherboard so it recognize the 7700K).
The 7700 will work too, it does/should come with an aftermarket cooler, it should be cheaper, but you will lose a bit of performance, not much. Going with the 7700K, an overcloking enable CPU, with your motheroard doesn't make much sense, but it will be the highest performance gain cause of its higher base and boost clock speed.
https://ark.intel.com/content/www/e...7-7700-processor-8m-cache-up-to-4-20-ghz.html
https://ark.intel.com/content/www/u...-7700k-processor-8m-cache-up-to-4-50-ghz.html
See this link to know where those procesors land, performance wise:
https://www.tomshardware.com/reviews/cpu-hierarchy,4312.html
And finally, whatever you choose (7700 or 7700K) it will be a huge, nah,
H U G E upgrade over your Pentium G4400.
Cheers