03 I35 idle/startup/running issues

[Quinoa]

Hey guys, I've been lurking here for a while and some issues with my 2003 I35 got me to register. I tried searching and came up with a few scattered results but nothing solid.
The car has about 168k miles.
So, problem 1:
-The car will sometimes die upon starting it up when already warm. Sometimes, it won't stay running after the 2nd and 3rd attempts unless i give it some gas. I searched and found that it could be the CPS (cam position sensor). Apparently that sometimes doesn't trigger a CEL, and I haven't seen a CEL yet. Are there any other culprits to this issue? If it is the CPS, how would I check/replace it?

Problem 2:
-Upon cold startup, the engine is noticeably louder than it used to be and sounds rougher. It idles slightly higher than the usual warmup high idle until it's warm. It isn't a rough idle in the traditional sense of a lot of vibration and the engine trying to die on you; it's hard to describe but it just sounds like an old GM 6 cylinder struggling. I thought a belt might be wearing out and looked around but found nothing out of the ordinary. Also if you try to move it when cold, esp immediately after startup, it bogs down/tries to die for a second once any amount of gas is given. I feel bad for the car when I start it up in the morning lol. When it gets warm, everything is fine and it idles quiet. No clue, please help.
edit: also, when moved cold and the bogging/dying for a second thing happens, I can smell fuel from under/around the car.

Problem 3:
The heater only works when the car is moving or when I'm giving it gas, and the AC only blows outside air at you in the summer. This is most likely a thermostat issue, but my father claimed to have replaced it not too long ago. I'll probably replace it again. Could there be any other reason this is happening?

Problem 4: At highway speeds, there is a slight vibration that seems like it's coming from the front wheels. It starts to appear at 65 mph, then it goes away around 85-90, and comes back around 105+. I'm thinking tie rods maybe?

There's probably more I'm forgetting, but I really need some insight to those already mentioned.

Thanks

[Quinoa]

No luck? I know the whole 'new guy to the forum is lazy, etc' stigma, but even the smallest advice would be appreciated.

[NutriaforBreakfast]

Have you ever changed the spark plugs?

[Quinoa]

Thanks Nutria,
They were changed about 9 months ago. I was also thinking about that as well.

[OwnerCS]

A couple of items I've seen that fit that description along the way that I would try cleaning and ohm testing are the Mass Air Flow (MAF) and the Idle Air Control Valve (IACV). A bad MAF seems to cause the car (when warm) to die at stoplights like it is running out of gas. I have experienced bad a IACV on other products that seemed to be more present when cold and also cause the car to lose power.

How many miles does your car have and where are you located? Do you have someone that can clean, test, and inspect the IACV? Cleaning the MAF is a delicate procedure as you don't want to break it.

Another suspect that can get neglected is the fuel filter.