How did the virus caught the systems, if they were offline?NO. As an example look up the STUXNET virus. It propagated through systems that were never connected in any way. Granted it was very targeted but the same prinicple applies.
If I have VPN enabled and there is encryption, can a virus still infect the system?
If I use a USB router or connect the PC to the phone, so it can gets internet from the phone that has mobile plan with secure and encrypted internet, can infection still happen?