I have asked my parents if I can buy a PS4 myself, but they say that I can play on my PC although the whole buggt. In addition, this should now be a family purchase for all… Do you have your own arguments for a PS4 and against the family purchase?
No, because there are no good arguments.
I have an argument against the PS4: Sony has announced that the PS5 will come next year. It does not make much sense then to buy a PS4. The games are traditionally not backwards compatible. New games will come for the PS5 and stand there with your PS4 and the old games, which are still limited.
Only that it will give backward compatibility. https://www.netzwelt.de/...s-one.html
Do I have to explain the difference between "hint" and "give"?
No, but you also sound absolutely. Anyway, it can be, but still you should, especially since you have the 400/500 euro determined (as a family), take the 5 Series next year.
If you pay her, she is yours and not the family. Otherwise belong the things of your parents also the family:-)