You go to the Immigration office where your staying, yes you can apply 2 weeks prior, its added to your 60 days stamp not from the day you apply. Not sure about copies at the office but most do have facilities to do it. You may also need the TM30 some office require some dont.
You could drop in to the immigration office and ask what they want.
Did you actually apply for a visa or just got the visa exempt stamp on arrival, If applying in Bangkok it would make a difference to the office you go to. Chiang Mia probably same office.