Multimeter Problem
You’ve described two completely different problems.
If the meter is switching from a reading to 0 during the same test, my first thought is you don’t have a good connection from the meter to one of the circuit wires. The battery could also be the issue as hamerfan noted, though I haven’t experienced that one.
Getting a value read in isolation and 0 in circuit tells me your circuit is either not complete or shorted - you’ve got a wire that is not fully connected, somewhere; or a short as GuitarDoc noted.