Rough Idle / Hard Start / Can't find Fuel Regulator

I have a 1997 eclipse rs 2.0L. I just recently got it about 4 months ago. We had to re-time it and replace the radiator. We replaced the fuel pump / injectors / plugs / spark plug wires. It has ran well until now. It did and still does have a problem starting. You can't really get it to start right away, you have to turn the key on for about 10 seconds and then it starts up perfectly. We suspect some fuel problem (pump) but didn't do anything about it since it didn't hurt how the car ran.

Just of late the car also idles very rough. I took it on a 200 mile run and on the way home it felt like I hit a small rodent or something fell off the car. I don't know if this 'accident' had any effect on the fact it now idles rough or not, tho.

A mystery to us is were is the fuel regulator at? All we can find at part stores/books is that there should be a fuel regulator on the fuel rail. It's not there. Is it on the fuel pump? Because that could explain why the new gas pump and how the car starts happened at relatively the same time.

We also question our new injectors. The first plug looks more burnt than the rest, but it's not very badly burnt either.