Can i plug pc on this apartment with older fuse box?

I would get advice from a local electrician that you trust. Nobody here can tell you if the wiring / fuses / whatever in that apartment are safe for use with any given load.

EDIT: This is particularly important seeing as you are buying the apartment. Never mind "can I use my gaming PC" - is it safe / do I need to budget for some electrical work would be higher in my thinking (impressed with your priorities though! )

You should be having an inspection done anyway before buying, which ought to include the electrical system, but presumably if the fuses and wiring are rated for the usual 15A/120V in the US (or whatever it is wherever you are) then it will support whatever normal stuff you plug in, just like anything with newer wiring. I'd definitely have a good UPS on important stuff, and surge suppressors on less important things.

"PC WILL BE: Rtx 4090,14900K,1600W PSU"

So that's towards the ragged edge of what a 15 amp circuit can carry if you hit the PSU maximums. Thankfully the 4090 isn't as peaky as the Ampere generation cards, but the CPU is a big and constant power draw on that system. You probably need an electrician to ensure that not only are the fuses safe, but that you know how many circuits you have, how big they are and where they go. 1800w is probably a realistic maximum for not overloading a 15 amp circuit, so PC + monitor + speakers etc. is likely fine if you have a 15 amp circuit just for the computer area, but if you try putting another high wattage device on the same circuit-- like a microwave, heater, air conditioning, air fryer, etc. you'll risk blowing the circuit and the fuse and that's Not Good. Old places might even have 10 amp circuits and that's also something you'd need to be very careful about.

If you can see problems like that in an old building, that may be the tip of the iceberg as in the early days of electrical hookups, they did a bad job of anticipating just how much the need for power in the future would be and you can run into strange situations where circuits are shared across places you might not expect. Hopefully it's at least copper wire and the ground actually goes to ground...

We don't know. Have an electrician, who can be there physically, inspect the wiring. An inspection of the house/apt/etc is generally part of the buying process.

I would never place a PC in a kitchen - any PC that's as fast as the one you mentioned WILL be pulling in a lot of air, and that WILL result in steam being pulled into your case and making your heatsink and fans sticky, likely eventually causing the heat death of the system.

We aren't realtors. Get the apartment you can afford and like the best. You are the one who has to live there.

There's no way to know where the circuits go by looking at pictures. If the building is really old, verifying that the power provided is decent is a good idea just because old buildings tend to have too few and too small circuits if they were never upgraded.

Yeah wiring that old you'd have to inspect to see if they even have Ground wires. No way to tell from the pictures.
By owning the apartment it would be 100% up to you to upgrade the electrical system and and that's why you have to figure that into the price.
At some point you'll get tired of replacing fuses because the quality of fuses for residential use is only going down.