Hello, I own a Mazda 3 2008 2.3L, 183,000K Miles. Ive owned it for about almost a year. I have 2 issues if you anyone can please help me. First, every time I start it (cold starts normally) the car fails to idle high to warm up. Instead, the car drops RPM below 1k and stays there and If I touch the gas peddle, the car usually stalls or if i do it slowly enough, it actually begins to warm up :/ I was thinking it could be the fuel filter or going bad fuel pump? Do these models even have a fuel filter? Second, as I am accelerating mostly from it being cold still, the car seems to accelerate very slow, as if the engine has some kind of build up. If I press it more it will take off normally, but there isnt really any smoothness. First gear there is usually a hard shift as well. When the car is fully warmed and I drive about couple miles it really doesn't do it anymore, most of the time is smooth, and shifts good. Please help

 

Is it fly by wire or throttle cable?