[Raynor]

I don't think it's reasonable to think that since this encounter and the Witch-King was scared by the events that took place, Sauron would believe any hobbit would be able to contend with his will.

Well, this would imply that Sauron thought the ring passed from one hobbit to another; I don't think that he has reasons to believe that. As far as he is concerned, the ringbearer survived from one attack to another and was still carrying the ring.

Sauron could probably see Pippin was quite terrified by him, but again Frodo was terrified of the Witch-King. Why would Sauron believe that since this hobbit was scared out of his mind it couldn't have been the Ringbearer then?

I believe it was more than fear: Sauron actually controlled Pippin through the palantir. Would he expected Frodo to be as easily bent to his will? Imo, if he trusted witch-king's report - no.

He put on the Ring several times. Frodo had shown that he did not have the will to resist the Ring's pull and the Ring was nearly revealed to Sauron because of Frodo (putting it on to escape Boromir)

I don't think that that this second part of your argument is related to the first one, since, in this case, Frodo didn't put on the ring out of weakness, but of necessity.

Knowing this, why would Frodo have the will to resist the pull to Barad-dur (through the Palantir), he didn't have the will to resist the Ring's pull to Sauron.

As a matter of personal opinion, it is easier for Sauron to control someone who has the ring, even if from afar, than to control someone through the palantir. It seems to me that our debate on Frodo and Pippin has moved this thread away from other members' interest, perhaps we could continue this on another thread.

Sauce pan: In any event, no one asserting that Sauron did not believe Pippin to be the Ringbearer has put forward any convincing explanation as to why Sauron (to Gandalf's mind) would be so obsessed with this Hobbit and why he would want him so urgently, if not only for information.

We know that Sauron was already obssessed with the ring; I don't think it is unreasonable for him to extend that to matters related to recovering the ring.

Also, to add, I haven't seen other suggestions as far as what is it that Sauron believed Saruman had (that wasn't his to have) and a Nazgul was coming to get immediately.

I expressed my opinion, in post #56, that:
In Unfinished Tales, The hunt for the ring, it is stated that Sauron was in great haste and fear when he heard that his enemies have captured Gollum. Apparently, he fears for anyone who has access to those with relevant information about the ring. Sure, he wants information for himself, but he also wants to hold off others from obtaining that information. I think that in this "others" we can safely include Saruman, of whom Sauron became aware that his servants waylaid or misled his own agents.
IIRC, in the Reader's Companion, Sauron was displeased at the witch-king's bringing his enemies closer to the ring, so this was becoming an increasing concern for him. To address your reply to my post:

he actually believed he (or Saruman) had something else of importance that wasn't Saruman's to have.

I don't think that we have already established that. If anything, neither Sauron nor Gandalf make _any_ referrence to the ring.