It is difficult for us to properly diagnose the problem in this case, without looking under the bonnet etc. What you need is some practical mechanical help from someone who can do this. For what you have reported so far, it is likely that a fuel leak persists somewhere.

Sold as seen means nothing people try to hide behind thinking they are smart. I would say if they mark up as sold as seen they probably knew about the problem. If the car had the problem before and they knew about it not that they would admit it they have sold you something un satifactory for purpose, aswell as something which is dangerous to your self and other road users. I would seek advice from trading standards about it.

It was a private sale so is was sold as seen. As long as the seller has not lied about anything he was asked thene there is no come back.