Hello All!
Peeps, thanks for advices! Actually, yes, the security update not only broke the AppStore, My Macbook pro mid 2015 started to work so slowly... I though it was damaged forever. like, You try to open system preferences, or a finder - and the mac runs this command like 2 minutes and everything is hanging. And, I was using the ElCaptain with the lates security patches and wanted to check the Catalina. So upgraded - and all my applications stopped working. Ten I returned to the latest 32-bit version - Mojave. ... And it's so buggy and slow. Literally, almost clean system with the security update (from the above) - and deal with it. So frustrated there was no help from apple at all...
But, I found something. If anyone gets the same problem with app store - there is a solution. Install the ONYX app and clean the system registry automatically using the instruction in the video. It solved the Appstore problem.
https://www.youtube.com/watch?v=5JcU1NHr-II&ab_channel=tHeLoVeOfGOD
And thanks everybody who participated! Good luck!