hot start issues

I have a 2000 metro. Recently it has been not wanting to start when engine is hot. I has just had a fuel pump installed last year, and I hear the pump when I turn the key forward, so I don't think its that. I should also mention it has bad valve seats, because it smokes apon cold start-up, but it has done this for years without incident. Also, randomly while driving, it acts like it has a loss of fuel and you have to flutter or floor the gas pedal to get it back to normal. I heard a small backfire or loud sputter once when this happened. But this situation does not happen alot. But I would think its all connected. Other than these issues, the car runs fine. Any suggestions on what I could check ? I don't have alot of tools or guages to work with, but I would like to troubleshoot as best I can first before taking it somewhere and getting charged crazy amounts of money. Any suggestions are apprieciated.

I had a somewhat similar problem. Mine turned out to be a leaking intake gasket. It wouldn't do it every time and always waited until the car was warm. It may not be your problem but I thought I would post.