In your opinion, can (should) Page be able to have kids if in this universe Alicorns having kids is very uncommon?

Will they be Alicorns?

Regular ponies?

Will they have human traits? Like dark Magic immunity?

Yes they should, Yes they would be alicorns, and Hybridize all the things!

7049639
Seeing how Flurry Heart came from an alicorn and a unicorn, I see him fathering alicorns.

Or perhaps foals of all four tribes like a pony-styled Echidna, father of all examples of ponykind.

I'd imagine he'd probably have alicorn kids. Dark magic immunity would be useful, but I don't think it would last 2 generations down the line, probably shifting to a strong resistance, being diluted by the pony blood. I think the kid would have the natural violent tendencies that a human would have as well as a more analytical mindset. Though it brings to bear the Nature Vs. Nurture debate.

7049840
As I see it: One Son from Sunset, one daughter from Luna.

Apollo, the Alicorn of Healing and Artemis Alicorn of Darkness.

I see issues with the creation of more Alicorns via mammalian means. An obvious one being, a race of immortal beings would quickly, relatively speaking, crowd out the merely mortal ones. I think a better solution could be that Alicorns can have children, but only when the world needs a new deity. This does of course make Flurry's existence far more interesting and impactful, but I see that as a good thing.