A US citizen can get a gun permit in Mexico that allows him to carry the gun for hunting. I sure wouldn't advise it with crazy TJ cops running around making up their own rules even if you had the proper paperwork.
The Mexican Constitution guarantees the right of Mexicans to possess arms just like the US second amendment, however Mexico doesn't have the 'NRA' so the constitutional rights have been severely restricted since the 60's when Mexico had civil unrest. The only thing I know for sure, if your a TJ cop or a drug lord, or working for a drug lord, guns are pretty easy to get from the US. The thing I love is the local gang banging cholo, is scared to get caught with a gun or knife, and has to resort to "choke holds" in order to rob gringos walking on that dangerous street Articulo 123.
Getting an apartment has nothing to do with being a Mexican citizen, however buying a house does, but even then you can still buy property in Mexico if you get a 'Bank trust.' However, it's better to become a Mexican citizen and not pay the extra expense.
I think the best way to become a Mexican citizen is marry a sex worker or better yet a 'ficha chica' who claims she never goes upstairs, but just drinks and dances with Mexican lonely workers who stop by.
Other then that I believe you have to live in Mexico for the last five years to become a Mexican citizen, and be able to prove it, you have to fill out a form and submit it along with your passport and FM-3 card. Lot of mongers have FM-3 cards, as as US citizens living in Mexico you have plenty of rights, and a FM-3 should be good enough for most people living in Mexico.
In the past if you became a Mexican citizen you had to give up your American citizenship, but you no longer have to. However, I understand that Mexican citizens aren't allowed to driver cars with foreign plates, so you might have to give up your favorite car. Personally I'd have no trouble giving up my American citizenship, but don't ask me to give up my car. ( the law may have changed regarding foreign plates?)