I would have the driveline u joints checked as well as the front end parts to start.
Check the universal joints and balance of the driveshaft. When you are accelerating pressure is applied to these parts and if they are worn or out of balance or dented they will cause a vibration that will stop when you let off the gas.
you need a front end alignment
Not to my knowledge, they only vibrate if they are heated
the 2012 mustang will run on regular gas
The 2013 Ford Mustang is a gas-powered vehicle.
The 2004 Ford Mustang is a gas-powered vehicle.
The 2002 Ford Mustang is a gas-powered vehicle.
The 2014 Ford Mustang is a gas-powered vehicle.
The 2011 Ford Mustang is a gas-powered vehicle.
The 2005 Ford Mustang is a gas-powered vehicle.
The 2003 Ford Mustang is a gas-powered vehicle.
The 2008 Ford Mustang is a gas-powered vehicle.