Although I don't think there is a definitive answer, only theories.

Gandalf certainly used his powers to help Frodo on Amon Hen, but lost contact after Frodo took off the Ring.  I don't think he lost contact because Frodo took off the Ring.  I think he lost contact either because Frodo was no longer in immediate danger and Gandalf could rest, or because the special nature of Amon Hen itself enabled Gandalf to maintain contact or both.  Most likely both, I believe, because we don't see any evidence of similar, palantir-like contact between Frodo and Gandalf after Amon Hen (although Gandalf is always thinking of Frodo, and in Tolkien's world that counts for a lot).

Sauron, I believe, looked towards Amon Hen in response to the call of the Ring.  Of course the Eye is always watching, but it does seem that by putting on the Ring and sitting in the seat on Amon Hen, Frodo has drawn Sauron's attention, almost as if he had used a palantir to look towards Barad-dur.  Again, I believe the special nature of Amon Hen has much to do with Frodo's danger of being seen.  Note that after leaving the seat and running down the hill, Frodo again slips on the Ring, apparently without drawing Sauron's attention.

“I dislike Allegory - the conscious and intentional allegory - yet any attempt to explain the purport of myth or fairytale must use allegorical language.  (And, of course, the more 'life' a story has the more readily will it be susceptible of allegorical interpretations: while the better a deliberate allegory is made the more nearly will it be acceptable just as a story.)” (From Tolkien Letter # 131.)