Legal Question in Criminal Law in California

Yes, the police may have found the gun on someone else and believed that you were a joint owner or they could have found a gun with your fingerprints. If no gun was found at all it is unlikely but not impossible that you would be charged.

Yes, you can be charged. Convicted depends on the other evidence. If they have witnesses who saw you with a gun, or a videotape of you with a gun, you're going to have a hard time explaining that to a jury.

Yes, if there is evidence that you possessed it illegally at some point in time within the limitations period. The evidence does not have to include the gun itself.