My 2009 Honda Accord begins to shake/ vibrate when i'm on the highway.. around 50-60 mph. I just had a wheel balance done to it and the vibration continues, by the way the car has 110k miles . I read that it could be bad engine mounts? Any help will be appreciated

Also when I shift between Park to Reverse to drive you can hear a thump, and I looked under the hood and I can see the engine move up and down when shifting between gears. I'm guessing the problem is bad engine mounts? Anybody has an idea how much it would cost to fix ?

It could be caused by the engine mounts being worn, but not likely. When the wheels vibrate at a certain speed it is usually caused by worn tie rod ends, or ball joints which any good shop should have picked up on during an alignment. It could also be caused by a bent steel belt(s) moulded inside the rubber on one or both tires.

I feel the vibration start around 50-60 when my foot is on the gas, but when i let go the vibration also leaves. I feel the vibration on the steering wheel.

That soounds more like engine and transmission mounts need changing. They are basically rubber, so should allow a certain amount of movement when changing gears or under load and off load, but should not be enough for you to feel it through the column. I would get a complete front end inspection done and also have them check the enging and trans mounts as well.