Yeah my experience has been that the Thai side generally doesn't have any photocopy facilities or at least claims they don't. I was once sent back to the Cambodian side to take some additional photocopies of my car registration documents at the Aranyaprathet/Poipet border while re-entering Thailand and that's the biggest and most popular border crossing between the two countries.
The Cambodian side does, because travelers on e-visas often need to print out a copy of their e-visa for departure (Cambodian e-visas are only valid for arrivals at some border crossings, not all, but for exiting the country any international border can be used).
Oh interesting. Maybe they do it for you on their phones. These helpers are also on the Thai side and yep, they're always Cambodian nationals. BTW Cambodian citizens need to fill out the form too, if they're using passports.
I doubt it, some borders are very small and don't have the space nor the personnel. Even at Aranyaprathet, they'd send you back to the Poipet side to print documents if you're re-entering there by car or motorcycle.
You will be receiving your entry stamp from Bangkok. The only way you could receive a Samui stamp is if your flight was arriving directly into Samui from Singapore or one of the few other cities which have international flights to Samui.