BudsGunShop.com - Can a non-citizen purchase this gun ?

Tin, ordinarily, Federal Law does not require such firearms to be transferred through a licensed FFL. So you can buy a black powder (i.e. muzzleloader, cap-and-ball, or per4cussion cap -- or flintlock, for that matter) rifle or revolver or single-shot dueling pistol anywhere. There is no background check, no federal form 4473, nothing. ***That said, I would check with the ATF or your local Chief Law Enforcement Officer, i.e. Sheriff or Police Chief.***

Tin, A non-immigrant alien who is not a permanent resident as a general rule cannot purchase firearms in the USA. There are exceptions for import/export, law enforcement and hunting but except for hunting, these exceptions are difficult to qualify for and if you do, you already know whether or not you can follow through.
Only citizens and permanent residents can purchase firearms freely subject to local, State and Federal restrictions. For non-immigrant aliens, non-residents can’t purchase guns at all. Borrow them, rent them but not purchase.
For non-immigrant aliens, those in possession of a valid hunter safety certificate in their state of residence and can prove said residency can purchase firearms for that sporting purpose. That means you can’t just purchase anything and you may be required to demonstrate why that Glock you want to buy relates to hunting. You will likewise be subject to all local and State restrictions and they may not permit a non-Green Card holder to meet their purchase requirements if they are allowed to do so under Federal law. Muzzle Loaders have Federal laws and separate state laws. You should search your specific state laws about muzzle loaders.