Is it safe for my grandmother to stop drinking cold turkey?

NO. Withdrawal from alcohol can be dangerous and mores so for weaker, older individuals that may have other medical problems. Seek help through your physician for this right away.
Depends. The limits that are set for our patients over 65 is 1 drink a day if she drinks more than this and can't cut back has to have an opener etc then before she does seek professional help. Bad outcomes can be seen at that age and over with concomitant medical and /or psychiatric problems.