OK, thanks.
I have figured out that in order to enable the host, i have to go to Setup/Hosts/folder with auto-discovery. Then select hosts to edit, then menu Hosts/On selected hosts/Edit attributes. On the top, in the path you will see something like “bulk operations”. Then on this screen, i have to change Custom attributes/Criticality to any other value from “do not monitor this host”.
Save, red crosses disappear. Apply the configuration using yellow button. Seems to work fine.