One month later after the topic was started and I finally fixed the hard start issue. It turned out the car was not starting well due to a FPR that was sending fuel to the faulty damper which in turn would send a little bit of fuel into the vacuum lines. Thus, I suspect that the fuel was "choking"/"drowning" the faulty damper that would other wise control the pulses of the fuel injectors. (I feel like this is incorrect

?)
I do apologize for not having shared my findings sooner, but work and homework have been hectic lately. But, here are some things I learned:
1. The car would actually start faster if I disconnected the vacuum line going to the damper as fuel would not choke the line.
2. The only reason why my car would start faster after working on it or leaving the battery disconnected was due to I somehow always leaving a fuel line open which would allow the fuel to evaporate and thus eliminating the potentiality of a hard start as I have now found out.
3. FPR was actually making the car run too rich (I measured a constant 55 psi on fuel pressure), which resulted in the smell of gasoline.
4. Rough idle was due to the injectors not pulsating correctly as the damper was not working well.
5. As a newbie, things get confusing,
After replacing both the FPR and damper with OEM ones from Z1, the car is running great.
So, all in all I do appreciate all of the help. Thanks guys!