1. Yes. It would. Happens all the time in cleistogamous orchids.
2. Yes. The offspring would be varied. When the chromosomes recombine, different traits are expressed.
3. Two identical plants (let's say two divisions of the same plant) would still produce variation.
If you take an Sc. Beaufort 'Elmwood' and do a selfing, none of the "children" would be 'Elmwood'.