You'd be surprised at the amount of fine military hardware that seeped from the former Yugoslavia into the whole of Europe (and continues doing so).
On the legal side, a number of countries in Europe have/are seeing growing registrations in shooting practices, in part because in some it is a prerequisite for gun ownership.
One key aspect, is that for several centuries most of continental Europe shared a distinctive cultural phenomenon : mass conscription, which for most was a byproduct of the Revolutionary Era and the rise of Nationalism. Until WW2 it was perfectly normal to own any kind of firearm in most if not all countries, the first restricting it being the dictatorial ones, with some exceptions (guess which subgroup was first forbidden the private ownership of firearm in interwar Germany?). The rise of massive guerrilla and resistance movements in occupied Europe was only possible due to a good number of available weapons and non inept users. Only after the conclusion of WW2, did some major countries restrict firearms ownership, where there was significant communist representation, for the left feared that reactionaries would be able to rise up against them if they were to be able to seize power democratically, and the right in turn feared that revolutionaries would be able to insurrect if the communists were to be able to seize power undemocratically. Other countries, which had less of an interior communist problem, but much more of an exterior one, developed huge militia-based armies and military-industrial complex during the Cold War respective of their sizes.
In my country, which is a rather extreme example of militia based army in the middle of Europe (dating back 700 year), in theory every 19y old youth is handed down a full auto assault rifle that become his personal weapon for about 10 years : after boot camp, he will take it home with the rest of his gear, be asked to go to shooting practice at least once as a civilian, and he will be called back for a month of service every year. Some years ago we were even handed down a can of ammo to store at home, the idea being to use it in case of war. After ending their service, those interested enough in shooting as a sport will be allowed to keep their gun, modified for semi-auto.
In the 90s they were clearing here the 500k inventory of WW2 era rifles, you just had to be a citizen and you could buy up to 2 for 100$ a piece with the bayonet (my dad got me one, wish we had gotten more). Roughly at the same time, there was an add in some magazine aimed at diplomats for crates of AK47 at 30$ apiece. Then later Yugoslavia broke up, and despite being a Communist dictatorship, they had some kind of a decentralized militia based military, which allowed for all the infighting, but also resulted, decades later, in vast amounts of fine weapons (AKs, RPGs, grenades, etc...), being available under the mantle all around Europe (in France legal ownership is such a hassle and expensive, more and more people simply don't bother anymore and get illegal AKs).
(the Brits are another story, for the longest time even their army was professional and their cops had no firearms).
Same as above.
There are many more democracies that have more guns per person than China. Now indeed if you look at Asian countries, and ignore Thailand which has the peculiarity of being the only one not having undergone colonization/unequal treaties, a good number will indeed have very small gun ownership rates, but notice that many are either former British or French colonies, and/or part of the Sinosphere, where it has nothing to do with democracy but with the long, very long history of power and the monopoly of violence in those lands : swords to plowshare/buddhas policies have been an instrument of power in both China and Japan since their very unifications, millenias/centuries before the advent of local civic liberties, and characteristic of the very pronounced top-down of their power structures, opposite to historical bottom-up aspirations in the West.
BTW, its in Hong-Kong that my asian-side forefathers sought and found refuge and arms for their fight against their colonial masters.