Palindromic time

A 24-hour digital watch has many times that are palindromic.

For example, 1:01:01, 2:41:42, 23:55:32, 3:59:53, 13:22:31, etc.

(Ignore the colons)

These curious combinations occur 660 times a day.

(1) Find the closest such times.
(2) Find the two palindromes whose difference is closest to 12 hours.
(3) Find the longest time span without a palindromic time.