Hot Water Absence in Bathroom Sink: Possible Strainer Issue and Unscrewing Process

There is no hot water in the sink in the bathroom. The shower is warm. Is it the strainer's fault? Only this tap is strange, how to unscrew the strainer from it? Thanks for your reply.

The strainer in the tap/spout is common for hot and hot water, but you can have a strainer on the valve to which the hose is screwed.
From a hose or hot water is leaking from the valve?
Hmm, is the valve open?

I'm also considering screwing it in, heh, my friend asked me for help, but I didn't have the tools. Something is wrong with the stove?

Anderstut wrote:

Something is wrong with the stove?

It depends, there may be more valves on the stove, because who can forbid a rich person? The stove is OK, because it does provide heat, but you can't see what's behind the stove.
For example, my friend, apart from the main valve, has valves for each tap, so turning off one only affects that one tap. There is no shower in the cabin.
You have to look. Here you can see that water is coming out of the wall so you need to check whether it reaches the valve and whether it goes to the battery.
Have you already unscrewed/screwed such a battery?

I guess a socket wrench will do the trick? Actually, I didn't do that.

A long, tubular socket, maybe a pair of pliers. The pin has a notch for a screwdriver. Generally, there is little space for a key there.
If it leaks from the valve, I would turn the hoses at the valves. It won't blow cold air, probably the battery. I haven't disassembled the head yet, so I can't help...

Do I understand correctly that when you turn the tap over the washbasin to the hot water position, no water comes out at all (no stream), or does it mean that when you set the tap to hot water, cold water comes out? If no water flows at all when you set the faucet lever to draw hot water, it is very likely that the faucet head is contaminated with sand or silt (there is a screen in the heads of such faucets). You need to either replace the cartridge (preferably) or disassemble it and clean it (contrary to appearances - the cartridge in such batteries can be disassembled, but it must be done carefully). If the cartridge is replaced, it must be the same one (to fit) - it is best to take the old one to the store or copy the markings printed on the old one. To remove the insert, you must first remove the battery lever (it should be screwed underneath with a small screw, usually with a small Allen key), unscrew the masking cover (by hand), unscrew the large nut pressing the insert with a wrench (probably a 32 mm or 30 mm wrench), remove insert (by hand - if it doesn't work, you can pull it with pliers). Of course, before all this, turn off the water supply to the faucet (valves on the hoses).