looks like a standard i3 - so the creality cr10 pro firmware would probably work.

In my experience with 5 totally different printers - stock firmware usually works more reliably than slapping the latest marlin on it.
I have yet to either want or need to change any of my machine's firmware.

sound's like you just need to sort the bltouch out - is it a clone ?
The cheap clones do tend to have issues and most manufacturers don't use genuine bl-touch parts.