So I can not add the apple care to my iphone after I bought it for 60 days?
You have 60 days from date of purchase of the iPhone to get Apple Care+.
After that, you cannot get Apple Care+.
And if you were to break the screen during those 60 days you would not be able to get Apple Care+ either.
Apple Care+ needs to be bought while the iPhone is in perfect working order, less than 60 days old.
The screen repair cost for an iPhone X is $279 U.S. Price may change if you are somewhere other than the U.S.
The display has been one piece since the first Retina display. You cannot change just the glass on any iPhone since then.
Nothing. You'll have to pay the out of warranty repair fee to get the screen fixed.
See here for details:
iPhone Screen Repair & Replacement - Official Apple Support
Apple Care + is a preemptive measure. You cannot buy Apple Care + after the device has been damaged anyway.
Can I buy a apple care after I bought the iPhone for half year?