Get the covid “vaccine”.... and test positive for covid a month later...that never fails

Probably the sane way they would do it in the US.

No

They need to come into close contact with an infected person.

They could just hang around obvious transmission hubs, tubd stations, buses, subways etc where difficult for any virus areosle particles to disperse. But you can't ever guarantee you'd be infected on that random chance

You may not know you have it because you may not show symptoms but you could still show positive on a test.

Touch a dirty shopping cart at the store.