Punctures or something else?

Leaking valves?

Would the car have been sitting on very lowly inflated tyres over time? Sidewalls may have perished.

Can you post up some pics of them? A tyre place should give you a good guide but if they were sitting for weeks or months at minimal inflation they could be a lost cause.

The poster means the Alloy wheels fitted to the car (referred to as "alloys" to save time). These can become porous due to corrosion and wear, allowing air to leak out very slowly, manifesting in a slow puncture situation. As another poster said, you can use soapy water on the alloy wheels to try and figure this out. If there is air escaping from the wheel/tyre, you will see it as a series of bubbles.

My advice would be to bring the car to a reputable puncture repair specialist and ask them to have a look at the wheels at this stage. They will be best placed to figure it out and should not cost too much for the diagnosis. In my experience, a puncture repair usually costs about €15 or thereabouts so unless you have to go replacing whole tyres, this would be the way to go if funds are tight.