2003 Mazda Protege LX high idle + vibration problem

I'm having a few problems with my 2003 Mazda protege LX @ 44,500 miles.

1) After I start the car, and the car is still in park, the car is idling around 1500 - 1700 RPM's and a humming noise is coming out of the front end. The normal idle for the car is apprx. 700 - 900 RPM's

2) When the automatic transmission kicks in, it's shifting at a higher RPM than usual. Through low gears to high, it usually shifts around 2500RPM's. Now it's shifting around 3200RPM's.

3) When I accelerate over 60MPH the front end of the car begins to vibrate and shake. The weird thing is that it's random. It'll happen about 70% of the time when I go over 60MPH. I'm not sure if this is related to the previous problem?

Thanks for your help.