Your friend who's a dealer was wrong. According to my dealer's handbook (yes I was a licensed C&R collector with dealer's privileges):
"An alien legally in the U.S. may acquire firearms
if he has a State of residence. An alien has a State of residence
only if he is reesiding in that State and has resided continuously in that state for at least 90 days prior to the purchase. An alien acquiring firearms from a licensee is required to both his identity by presenting a government-issued photo identification, and his residency with substantiating documentation showing that he has resided in the State continuously for the 90 day period prior to the purchase. Examples of qualifying documentaion to prove residency include : utility bills, lease agreements, credit card statements, and pay stubs from the purchaser's place of employment, if such documents include residential addresses.
C.F.R. (Code of Federal Regulations, the federal law)"
[18 U.S.C. 921, 922(b)(3), (d) and (g) 27 C.F.R. 478.11 and 478.99(a)
All bold emphasis are mine. The point of it all being that after a period of 90 days (and having acquired a government issued photo ID such as a Driver's License) as well as a long term lease and job (which can only be gotten with a resident I.D. card; the "green card") an alien has essentially established permanent residency. The 90 day period is exactly the same as required foir a native citizen to establish residency in a new state (or even a new county or town) for voting purposes.
Furthermore the form you have to fill out when buying a firearm (A.T.F. Form 4473) has a series of questions the buyer must answer. One of said questions (number 15) specifically requires aliens to provide their U.S. issued alien number or admission number. Here's a link to the form
www.atf.gov/file/61446/download As you can see, there are some exceptions for properly documented sport hunters and a few others.
Regarding importing a firearm here I've only ever done it once when I returned from England. All I had to do was fill out the Customs Declaration; but that was a shotgun I had originally bought here and had taken out of the country with me to England when I was stationed there.