Do you think that James Watson and Francis Crick should have received the credit for determining the structure of DNA?

Yes. They put the pieces of evidence together and wrote the key paper. It's true that many of the pieces were generated by other people, including Franklin, and it's possible that some of these people might have eventually figured it out, but they didn't. Watson and Crick did it first. That's how science works.

Yes they should. They determined its structure. It's sometimes said that their work was based on others like Franklin. But, that's all it was. Gathering disparate evidence and putting it together. Scientists don't work in a vacuum. Everything that's done builds on the knowledge that already exists. Crick and Watson were the ones who put the evidence together and correctly identified DNA's structure. Could that have happened without knowledge generated by others? No, of course it couldn't. But that doesn't mean that they shouldn't get the credit for discerning what the evidence was saying.

If you are pushing the idea of Rosalind Franklin, the Nobel Prize for DNA structure was awarded in 1962, she died in 1958. The Nobel Prize is not awarded to dead people. Aside from that. it was not until 1961 that sufficient evidence had accumulated to show that Watson, Crick and Wilkins were correct back in 1953. If you have read the original paper in "Nature" there is very little information in it, there are barely two pages.

There may have been an occasion when the prize was decided but the intended recipient died before the prize was actually awarded.

Yes. Their contributions include: complementary base pairing, antiparallel strands. They really did discover stuff by building a good model.

Franklin, Wilkins, Chargaff, and Pauling did not discover those things. Franklin & Wilkins might have, if they'd been working together and building models.

No.