There are no admission requirements to terminals. You need a same day boarding pass (with exceptions not relevant here) for a departure from ORD to gain admission to the airside area. Terminal is irrelevant. You may be asked at a security checkpoint, but that it only because most people entering the "wrong" checkpoint really have made an error.

No, there is not quarantine or other requirement for Chicago, including ORD, for those passing through. While this is not a connection (two separate tickets), that is not relevant for Illinois or Chicago rules.

Make certain that you have a lot of extra time for the transfer. On separate tickets you have no protection if you miss your UA flight.