Bmw 530i 2004 E60

[dnh2006]

Ok 2 things i need opinion about before i take it somewhere and they rip me off.

At low speeds my car has some vibration , if im going at a constant 60 km/hr the car tends to vibrate a bit and the steering wheel shakes.

When i accelerate from like 0 - 60 and i let go i find that sometimes my car stays reved up and takes a while to come down. My fuel consumption meter also stays up even though i let go on the gas. Anyone with similiar problem?? I thought it was the transmission but it shifts normally wen im accelerating so im confused. Can anyone provide help

[witeshark]

For the shaking, I think I'd have a look to see that the wheels are balanced. As to the engine lift off lag, maybe there is a throttle control issue, could be it's sticking somehow.