Odd vibrations

[3series]

Hello all! New to the 318ti scene, and 4 cylinders for that matter. I've previously owned an e36 coupe and currently own an e46 coupe as well. I can't seem to operate the search button, so point me in the right direction if these questions have been answered. I'm fairly long winded, so bare with me. In first and second gear of my 5 speed manual I can feel a vibration that seems to come from right rear wheel or differential. I've experienced this same problem in my e46 but have never found a reasonable explanation. The ferocity of the vibration is dependent on how hard I am accelerating but only appears in the 2-3 thousand rpm range. It does seem to be worse on hard right hand turns. It feels as if my wheel may vibrate off. My first thought was cv axles but it just didn't make sense as to why it only happens in 1st and 2nd gear from 2-3 thousand rpms. I plan on installing coilovers and lowering springs but don't want to before fixing this problem. Second vibration comes from the engine compartment shortly after cold starts. The vacuum pump comes on then the engine rpms fall and a weird sound and vibration comes from the engine. Sounds as if a pulley is about to rattle off. After 5 seconds to 1 minute there is small squeak/errp and the sound and vibration vanishes. Only to appear at the next cold start up. The vibration/sound will stop if the car goes over about 2000 rpms. I figure this a pulley or tensioner failing. Thanks in advance for the assistance guys.