* You need a copy of your passport to buy a ticket at the counter. You don't need your actual passport.
* You don't need your passport to board the train.
* Although in Thai law you should always have ID with you. In practice this usually (but not always) means that also a copy is okay, or a Thai driver's license is ok, etc.
Yes; doesn't matter if it's your first, second or final extension. It will all get auto-extended to April 30 first, and then later we'll hear what's up after that.
Chiang Mai office clarified that they apply it to any kind of visa or extension of stay. All automatically extended to 30 April, without charge and without the need to visit.