We can help on all of those issues. We can go into more detail, but here are the short answers:
Slow start due to either weak fuel pump, or leaking check valve in the fuel pump (fuel lines empty out into the fuel tank), *OR* fuel injector(s) leaking, draining the fuel rail into the intake and one or more cylinders. If leaky injector(s), it/they might have a little dirt in the injector pintle (thatís the magnetically driven pin the goes in and out of the valve seat to close and open the injector). Sometimes you can get rid of that by running a dose of Techron or Sea Foam through a couple of tanks of fuel, but that doesnít always take care of it.
Hereís a little trick with that until you figure it out and get it fixed: Before you start it, turn the key to Run position for 3 to 5 seconds, then turn to Off for 3 to 5 seconds. Then turn it back to Run, then back to Off again. Then crank it - it should start.
(Explanation: The engine computer only runs the fuel pump for a second or so when you first turn the key on, and then keeps the pump off until the computer detects that the engine is running. With the fuel lines drained due to either the fuel pump check valve or the fuel injectors leaking down, one short run of the fuel pump at key turn on isnít enough to get fuel to the engine. But turning the key On and Off a couple of times before cranking runs the pump enough to fill and pressurize the fuel lines and fuel rail, so it will start much quicker.)
It may sputter for 2 or 3 seconds and then smooth right out, but it will start much quicker. If the fuel pump is weak (rather than leaking check valve or fuel injectors), the key On-Off trick probably wonít help. That can be checked by measuring fuel pressure (thereís a port on the fuel rail to plug a gauge into).
Fuel filter - designed to last the life of the vehicle - built into the fuel pump, so was replaced with the fuel pump. The fuel filter should not be causing any problems. If the fuel filter were partially or mostly clogged, youíd be complaining of the car not having any power when you try to accelerate, and I donít think you mentioned that.
Oil light - let me guess: when youíre sitting at a stop light, idling in gear after the engine has warmed up, the oil light flickers or comes on solid until you accelerate. That, or the light glows dimly sometimes when going down the road - or some of both. Both problems will be fixed by replacing the oil pressure switch - do not use aftermarket for that part - they often have problems right out of the box - dealer only for this particular part. When you replace it, spray some brake parts cleaner all over the connector and wire to remove any oil - really wash it off good. Then let it dry thoroughly, and plug it back in. The dash light is an LED that takes very little current to light up, and oil in the connector leaks enough electricity to dimly light the LED. Oh - and donít be surprised if thereís oil dripping from the old oil pressure switch when you first look at it - sometimes they develop an oil leak, sometimes they donít.
You and your mechanic sound like you have your act together. Everything he told you exactly fits with the above. Show him this post and he can probably take it from there.
Well - I guess I filled in more details than I planned to.