"I would buy a new car."
Translation:Baswn i'n prynu car newydd.
It's fine grammatically, yes: Prynwn i gar newydd. However, the short-form conditional is limited in colloquial language to certain verbs, things like: hoffwn i "I'd like", dylwn i "I should", gallwn i "I could", dwedwn i "I'd say", meddyliwn i "I'd think", synnwn i "I'd be surprised", etc.
Any verb can take the short-form conditional in literary Welsh, plus some dialects make wider use of it in the colloquial language, particulary in the south-West: ysgrifennwn i "I'd write", elwn i "I'd go", delwn i "I'd come", gwnelwn i "I'd do/make", celwn i "I'd have/get". (Note in spoken Welsh in all dialects that the -wn i ending is invariably pronounced -en i: dylen i, synnen i, elen i etc.)