I don't have time to go into these in detail. In fact, I didn't even read the second one. With regards to the first question, though, I don't think that Clammy can claim the prize for fishing up the handcuffs because the reward did not induce his actions of finding them. He didn't know about the award. (see Broadnax v. Ledbetter) -- Merely performing the things called for without reference to the offer is not consideration towards the offer.
He didn't know about the offer at the time he found the handcuffs, but he did know about the offer at the time he turned them in. The ad indicates that a reward will be given to anyone who returns
the handcuffs -- not to anyone who finds the handcuffs. Acceptance would be by returning the handcuffs, not by simply finding them. Clammy returned the handcuffs after learning of the offer. This would then operate as an acceptance, unless he manifests a subjective intent not to accept by his performance.
The next question is whether the offer was for the return of any of the three pairs of handcuffs involved in the incident, or just one pair (the one Braverman wriggled out of and kept). The offer isn't clear on this. Applying the objective test, C could argue that a reasonable person would read the offer to mean that C only wants one pair of handcuffs -- the
handcuffs. Clammy could argue, on the other hand, that a reasonable person would have assumed the offer was for any of the three pairs of handcuffs. Each of these arguments seems plausible.
If the offer is read according to C's interpretation, then C wouldn't have to pay Clammy the reward, because his returning another pair of handcuffs wouldn't be a valid acceptance.
If, however, the offer is read according to Clammy's interpretation, then C does have to pay Clammy the reward. Clammy's actions would be a valid acceptance because he did what the offer requested.
Under either reading of the offer, C would still have to pay Braverman. Whether C was seeking the return of any of the handcuffs or just the most famous pair, Braverman's returning the handcuffs would be the performance the offer requests and thus a valid acceptance.
If the offer is read as seeking the returning of any handcuffs, then there is still another pair of handcuffs out there and C could have to pay another reward. A press release wouldn't be sufficient for a revocation of the offer. To revoke the offer, C would have to publish an ad in the same paper or papers that the original ad ran in back in 2001. This revocation would be effective even if not all the people who read the first ad read the second one; the revocation is assumed to be communicated at publication, just like a revocation is communicated if the unopened envelope is put on your desk. C probably wouldn't have to run the revocation ad for as long as the original ad ran, but it would have to be for a reasonable time and would probably have to be similar in size and placement to the initial one (e.g. if C took out a double-truck A section ad the first time, it can't revoke by a small classified ad in the back pages).
I don't think Clammy could make a promissory estoppel claim because there's no information that he relied on the offer to his detriment. As for a quasi-K claim, Clammy would have to prove 1) that he conferred a benefit on C with no intent of acting gratuitously, and 2) that C had an opportunity to decline the benefit (or there was a reasonable excuse why not). Here, Clammy's actions brought a large stream of publicity, which is probably a benefit to C. C may or may not have had opportunity to decline the benefit; it could have told Clammy to go away, but a media frenzy is rather hard to stop. If it had no chance to decline the benefit Clammy conferred, the very nature of the publicity may be a reasonable excuse why no opportunity existed. To get restitution, Clammy would then have to prove how valuable the benefit he conferred was. This might be a bit difficult -- you'd have to ask whether C's business increased afterward, and by how much.
[disclaimer: I'm also a 1L, and my Ks exam is tomorrow.]