their ages / birth dates fit - Hermione's birthday is in September, Harry's is in July,and must be almost a year after hers (because she is eligible to take the Apparition test, but Harry isn't old enough yet);
Nothing about their age and birth-dates is especially eye-opening. You could just as well develop a theory that Cho was related to Harry based on age alone.
there are so many similarities in wizarding talent and abilities (best students in their year);
There aren't really a lot of similarities in Wizarding talent, in the least. Evident after they've taken their O.W.L.s as well as throughout the books in general. Hermione has always been talented in the practical, lesson based magics, as well as having an affinity for the academics. Harry's talents lay elsewhere.
his explains why Hermione is such a talented witch (she isn't "muggle-born" at all, but was adopted because James & Lily for some reason had no alternative but to do so - for her own safety and security???);
There are two reasons why this is makes no sense. First, Hermione is older than Harry, why would James and Lily have hidden her, and not Harry as well? Secondly, you say "Muggle-born" as if her talents are not conducive to Muggle born wizards. No where in any of the books does it ever make mention that Muggle born wizards or witches are inferior in skill.
this outcome means that Harry & Ginny will get back together, and Ron and Hermione will finally get together, and no-one will be disappointed (because they will all end up related, and Harry finally will get to have a real family which is genuinely "his");
I don't see how the theory supports this, the normal story arc does so on its own and does not need these relationships to be realized in order for what you mentioned above to come to pass. It would be perfectly within reason for Ginny and Harry to get back together, and for Hermione and Ron to hookup, without there being any blood ties between Harry and Hermione.
they even look alike (dark hair with a mind of its own!!!).
Hermione has bushy hair, no where has it ever said it had a mind of its own - like Harry's. And other than that small, infinitesimal comparison, nothing of their other features comes close to being similar; had there been, J.K. would have had the foresight to elude to this throughout the books, so that the revelation of them being related made sense and didn't seem like one of those cheap moments in literature where the author manifests a plot twist on the fly to grip his/her readers.
I suspect that in book 7, either Aunt Petunia will reveal this (as something she had no compunction about not disclosing before), or Harry will discover it as a result of going to Godric’s Hollow.
People give Aunt Petunia too much weight. She's either going to turn into an ultra-powerful super-witch who can shoot fire from her nostrils and reshape space and time, or she's holding the secrets of the Ark of the Covenant and knows the exact location of Santa Claus's Summer home. She knew a small amount of information about the wizarding world, no more than I would suspect anyone who had had a family member that died as a result of magic and wanted to know at least the "how" and the "why."