So, at the grammar page I can see that the subjects for he and she are 'rok' and 'rek' respectively, and that this is indeed canon. But when I go down to the objects, I can see that his and her are 'rok' and 'rek' again, but this time it says it's non-canon.

So how is this? We know that the subjects for 'he' and 'her' are 'rok' and 'rek' officially, but the objects for those two pronouns hasn't been heard nor written by an official source? So we have to guess it's the same?

Supossing that both subjects 'rok' and 'rek' are canon, does this mean that there are female dragons? Because I can't remember anything from my adventures in Skyrim regarding to dragon genders, even less to female ones. Do they reproduce or how does it work? How do we know that 'rek' is the pronoun for female dragons, even if female dragons are a thing?

Because it sounds really strange to me thinking about female dragons and how it could've been proven that they indeed existed and that 'rek' is that pronoun. Because whenever I'm learning about the language, both 'rok' and 'rek', mostly the second one, sound really off for me. As if they had been a non-canon english-fication of the dovahzul language, since most of other big languages (Spanish for example, my native language) use the same word for both 'his' and 'hers'. And it gives me the feeling that the dragon language would be much closer to using this last method than having two different gender based object pronouns.

Thanks.

EDIT: Fixed two interrogation marks

Are there female dragons?

Same thing as with male dragons - no. Unless you count the half-speculative Jills, which are timeline mainainers sent by Akatosh during Dragon Breaks and aren't technically even the same species. Dragons are divinely created and immortal, they do not reproduce sexually or otherwise.

What's the deal with rok/rek then?

It seems most probable that rok is really gender-neutral and rek is a Nord invention. Dragons only ever refer to one another as rok (Dialogue 0009C218, 000556DB, 00048F05). There is also no gender distinction in the third-person singular possessive suffix -ii.

How do we know what the object pronouns are?

Our current practise is based on simplicity and analogue. Because all known object forms for nouns are identical to their corresponding subject forms, it seems sensible to do likewise with pronouns and only mark participant roles using word order. The only hitch is nust/niin 'they/them', and even that is found on a human-written Word Wall.

To sum up the above, your thoughts are the closest to correct we can know.