Steering Shake after 60mph

Bad motor mount? Sure that the shake is not coming from an unbalanced wheel with a corresponding shaking in steering wheel?

Get a wheel balance first and when the balance is being done get them to check if the tyres are out of round

I'm guesing you have had your tires balanced and wheels aligned. If this does not help, then you have a broken belt in one of your front tires.

Most likely you lost a weight from one of the tires. It could also be caused by a bad or dry component in the steering ( tie rod end, bushing, etc.) First I would remove the tires one at a time and check the rims closely for a clean spot where a weight was. Then I would check the steering and suspension components for shrunken or dry lubrication points. Then I would make sure the wheels are straight , back up about 10 feet or more and look at the tires to see if they lean one way or another.
Typically, if it is a weight issue, the shaking would start around 45 mph or so, so I would suspect a dry lube point either in the steering or suspension.
Hope this helps!!

Odd question

Where does safety come in here?
All tire mfg make safe tires for your car

That said there are some that won't be so good
on it

Pirelli's are too hard a ride in my opinion

Tire Rack is the place to look & read reviews

Then go to at least four stores to look at tread designs

I would suggest you look at cooper tires if they have your size
in the tread you want

Goodyear are too expensive & so forth etc

Take your time doing some research

The shaking may be remedied by having your tires balanced
I have no idea what "Guatemala" means in this context
Sounds like you're asking about a temperature guage that is faulty or a faulty sending temperature sensor

oopps! will you please check your tires if there is bubble cause of over filling of air or maybe to much air. Try to feel it using the sense of your palm, just the top only not the side of the tire. Do not use your vision because sometimes you can not see it, just feel it by your hand.

that happend to me in my eclipse you just need to get them aligned past 60mph and they will be fine.

It is only a stabilizer problem and I also suspect that you got bad tires. Also your steering rack can be checked on. Cheers

I would suspect vacuum leaks of faulty emission components.