I've heard that Northern Ireland has lenient firearms laws. How does buying a firearm work there? Is there a waiting period like here, or can you just go into a gun shop and purchase one?
The Northern Ireland licencing system for a firearms certificate is more or less the same as the rest of the UK. You have to demonstrate a "good reason" for each firearm you wish to own, i.e target shooting, hunting, collecting, in rarer circumstances personal protection. Once the authority for said firearm has been granted on your certificate, it is simply a matter of going into a shop and buying that type of firearm. No waiting period
per se, besides waiting for the police to process your firearms licence (which varies greatly depending on the individual police force and how much of a back log they might have).
One thing that is significantly stricter about Northern Ireland compared to the rest of the UK, is that crossbows and air guns require a firearms certificate (they are unlicenced in England, Wales and Scotland and can be bought by anybody over the age of 18).
Also the Northern Ireland licencing system differs slightly in that it has only one licence catergory, where as the rest of the UK has two catergories. As follows:
NI
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Firearms Certificate - Covers rifles (single shot, bolt action, lever action, .22 semi auto), all shotguns, handguns, air guns (including paintball guns iirc), crossbows, black powder weapons.
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No licence - Bows, slingshots, airsoft guns, blank firing guns.
Eng, Scot, Wales
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Firearms certificate - Covers rifles (single shot, bolt action, lever action, .22 semi auto), high capacity and detachable magazine shotguns, short barrel shotguns (<24 inch barrel, not semi-auto or pump action), high power air rifles (above 12ftlbs), black powder handguns, long barrel handguns, cannons with a bore over 2 inces (Yeah, you can't own a little .22 pistol, but you can own a cannon...)
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Shotgun certificate - Covers single/double barrel shotguns, semi-auto/pump/lever/bolt action shotguns with a non-detatchable magazine and a capacity of 3 or less rounds, smooth bore muskets, cannons with a bore less than 2 inches.
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No licence - Air rifles (<12ftlbs), air pistols (<6ftlbs), crossbows, bows, spearguns, slingshots, paintball guns, airsoft guns, blank firing guns.
Note, shotgun certificates are simpler to get than a firearms certificate, and the conditions upon them are less stringent, most notably, once you have a shotgun certificate, you a free to purchase as many of the firearms it covers as you like. You don't need to demonstrate any "good reason" for each gun, though registration is required.
So that's pretty much the basics of British/Northern Irish gun ownership, as far as I understand it (there are other details surrounding antiques/obsolete calibre weapons, and various exemptions and ambiguities in the law which I won't get into right now). Hope I haven't confused anybody too much.