So I just bought a 95 infiniti Q45 with 300,000 on the body but engine has 80,000 and the transmission has 60,000 on the rebuild well a couple days after I bought it it started to randomly die. I asked the guy I bought it from n hee said it was the fuel pump that he already took it in to get it checked out. well I put in a new fuel pump and filter today. And it still keeps dying on me idk why its dying on me I haven't noticed any patterns of when our how it dies but once I was driving on the freeway about 60 miles an hour and the RPM's dropped all the way to 0 and then came back on but that only did that once but any other time it dies it shuts off and then it won't start for a little bit but if I way it will turn on after like 5 min idk what it is but it keeps dieing I love the car so I really would like to fix it any idea what could be wrong

welcome to G50 ownership. few 20+year old cars can be as satisfying to drive.....
you will help yourself a lot by searching.
could be a lot of things, you must research and provide data to get the best help.
do you hear the pump humming (key/on, engine off)?
what is the measured fuel pressure?
could be FPCU, but we simply don't know from your description.

as I recall from Dr.Jay's old posts, usually the FPCU goes bad when the fuel pump isn't working, so if you had a fuel pump replaced, then you should go ahead and inspect/replace the FPCU

Check your CPS. When cold it's fine,but at 200 degrees it seems it's going wide open Hence no start condition till it cools back down.

wouldn't the CPS throw a check engine Light?