Small Engines (Lawn Mowers, etc.): John Deere RX63, fuel caps, fuel filter

Question
I recently purchased a used John Deere RX63..the owner said he could not get it to start.. I took the card off and cleaned it, replaced the spark plug and it cranked and ran..I also replaced the fuel filter..while running it it would start to die I would look at the fuel filter and it would have no fuel in it.. I would tap on it to get fuel back in it and it would keep going. I parked it and the next time I used it I looked at the fuel filter and it was full of gas.. the mower started right up and began to mower.. then it began to die again..looked at the fuel filter again and was about empty, I shook it until gas waas in it again.. I ran out of gas so at that point I replaced the fuel lines and the fuel filter because the line needed replacing and the filter had particles in it.. it ran for a while but then died again.. the new filter had particles in it too..I could not get it started again..it was as if it got to hot..I checked the cap for ventilation and trying bowing compressed air to see it the vents were clogged..I am not sure it they are or not.. I would think that even if it was that it would still get air from the overflow line.. also could the fuel line be to long..I cut the new line about 2 inches longer.. and can you tell me which screws on the carb adjusts what

Answer
What engine is on the unit?  I have had bad fuel caps...not venting and stopping the fuel flow.

Does the engine have a fuel pump?  If it does then you will have a couple of lines.  If there is no fuel pump then the gas line will go directly to the carb.

Will it run if you loosen the fuel cap?
Is the tank full, half full or not very full when the mower acts up?

Let me know.
Eric