Whats wrong with my car?

There are a number of things that could cause this. You could need your tires balanced and rotated, you could have a bad ball joint, you could have a warped rotor, you could have bad tie rods, etc. Most likely you have a tire out of balance.

At 60 mph when you develop a wobble it generally means that you have a bad tire.

I found a great article for you at this site. It is a few pages of explanation. It is right out of the book.

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Tire balance, damaged suspension components, or the vehicle needs an alignment.

Sounds like a separated tire , it should do it at 10-15 mph also

Sounds like your alignment is off. You probably just need to rotate your tires.

Does the steering wheel shake at 60,or the whole car?
if the steering wheel does its in front , if not ,rear (tires , rims, ect)

I would say you have a bad tie rod(s). Fortunately it's not an expensive repair.

Has YEEEEEEEEhaw says. Your tires are way out balanced and alignment.