When I start it for the first time each day, I hear the fuel pump buzz and it fires right up. Then, any other time I try to start it, it's really hard/impossible to start. Big clue could be- I don't hear the fuel pump buzz again.
This can happen just minutes after I've initially started it/turned it off. Or way later in the day.
Also, it has a slightly shaky idle when cold but runs really good after it's warmed up.

The only thing I've checked for is vacuum leaks.

Could it simply be the fuel pump relay? or something else. The fuel pump relay isn't the original...