can an 870 chipset mobo be replaced with an 890 chipset mobo?
More aboutmobo replace
If you replace the mobo, sure, can be do it.
Yes... 890 is an upgrade to the 870 chipset but unless you are needing Crossfire support of at least x8,x8, there is no need to do so (even less of a need if currently running the ASRock 870 Extreme3).
You will need to do a fresh install of the OS, with the move to a new motherboard (well... it is highly recommended you do!!)
Yes, they would be compatible. I would recommend a complete Windows re-install just to make sure there aren't any driver issues.