What characters could make a claim for the throne and a couple hypothetical situations (for potential future stories)

I have a question about how the Claims for the Iron Throne work?

If Shireen Baratheon had made it to adulthood would she have a claim for the Iron throne

Now some hypothetical question

If Bran Stark and Myrcella Baratheon (for this hypothetical King Robert I Baratheon is her father) had gotten married and had a child could that child have a claim for the throne

and finally did Gendry have a claim to the throne after he was legitimatised