Can you legally own a fully automatic vz58 or AK-74 in Slovakia?
Here in Austria everyone of legal age (18) with a registered residence in Austria can buy bolt action rifles (Kat. C guns - rifled barrel) or single and double barreled shotguns (Kat. D guns - smooth barrel) - so in general stuff that could qualify as hunting rifles (but also includes precision rifles etc. as long as they are not semi- or fully automatic).
If such a person already owns a weapon-related permit like a hunting license, WBK or WP he can buy the stuff right away - if the person doesn't have any weapon related permit there is a 3 day period after which the buyer can pick up the purchased gun. During that period the gun dealer must check if the buyer is not restricted from owning a gun - for example because he was in prison for a certain period of time or similar.
Then we have the so called Kat. B guns which include all types of modern revolvers, pistols, some semi automatic rifles (only a very few "military style" semi automatic rifles are legal in Austria) and some semi automatic shotguns. To own and transport such guns you need the WBK or Waffenbesitzkarte. If you want to carry such a gun, you need a WP or Waffenpass, which is Austria's "carry permit" (does not distinguish between concealed and open carry - but I highly advice against open carry until you are wearing some sort of uniform or something along that line) and almost impossible to get nowadays. The WBK and WP allow you to own a very specific amount of Kat. B guns - normally you start with 2 and over time you can ask the authorities to increase that amount - if you are able to convince them that you really need more guns e.g. for different types of sports shooting disciplines.
If you own a WBK or a WP, the authorities want prove from you that you shoot/train regularly (e.g. a shooting diary together with a confirmation from the president of your gun club), otherwise you will have to make the "Waffenführerschein" every 5 years. If you own an Austrian hunting license as well, this prove is not required.
Kat. B guns require a higher level of security regarding storage but the absolute minimum you must assure with every gun is to keep it out of the reach of people that are not entitled to a gun themselves - like minors etc.
Last but not least we have Kat. A guns - mainly military weapons that cannot be owned without a very rare, very special permit. All semi automatic rifles that are not Kat. B are automatically Kat. A - and even pump action shotguns are considered Kat. A - despite the fact that you can legally own a semi automatic shotgun with a WBK. Yes, it makes absolutely no sense, welcome to Austria!
I think this should get you started