I need to have many toe nails removed. Could I ask my doctor to give me versed instead of painful local injections?

Yes. But you will still need the injections for anesthesia but you won't care. This will also need to be done in an outpatient surgery center.
Yes. You could ask. If you are very anxious then it may be helpful. You would still need a local block, you just would not care that it is happening.
Probably not. Not unless you have a really high pain threshold ; you need the local to numb the nail bed; the versed offers no pain relief.