"I cannot buy new clothes."
Translation:Ní féidir liom éadaí nua a cheannach.
The 'a' with a fada in an earlier construction meant 'at its'. What does this 'a' without a fada literally mean?
This a is a preposition that literally means “to”, in the English infinitive particle sense of ”to buy”.
No - the "infinitive with an object" construction is always object + a + Verbal-Noun.
What you were trying to get to was probably something like Ní féidir liom ceannaigh éadaí nua, but that that's not how this type of sentence is constructed in Irish, even though in English you can switch between a non-infinitive construction ("I can't buy clothes") or an infinitive construction ("I'm not able to buy clothes" or "It's not possible for me to buy clothes"), you need to stick with the infinitive construction in Irish (with the object before the verbal noun).