Is it possible to make old tiles look beautiful again? With tile paint?

Yes... Since we don't know if the tiles are sealed, we have now decided against tile paint. Question: We now just want to lay vinyl. Is it absolutely necessary to level the joints between the tiles for this? Or would it also work if we lay impact sound insulation underneath? We are a bit apprehensive about the work involved in leveling the joints. There is still a little space between the door and the tile.

The joints will press into the vinyl over time. I would apply thin-layer leveling compound on the tiles and then put the vinyl on top.

Then you won’t have any more problems with the old joints.

Stupid question: Spread it on the tiles, meaning just apply it over a large area, or apply it in detailed fist-sized work on the grout lines so that everything is level?

Stupid question: Spread it on the tiles, so just apply it over a large area or work on the joints in small-scale detailed work so that everything is level?

Of course, roughly go over everything. Basically dump the bucket in the middle of the room and pull it across the surface with the large squeegee/water blade.

Thin-bed leveling compound is generally self-leveling and also self-levelling. You don’t need to trowel anything off. You could apply primer to the tiles beforehand.

Can a complete layman do this or should we better hire an expert?