Is buying a car, maybe a 2nd hand car a financially irresponsible thing to buy? Supposing we have saved up $$ for it?

Yes unless needed

Depends on ur needs...

Quite extreme to label that, I think look at your family situation then decide. Ignore external comments who do not know you.

Weigh up why you need a car. factor in also your own effort in driving vs being driven (ride hailing/public transport)