Never Let Me Go, Shake It Out, No Light No Light, and Spectrum (to an extent), among others off of her Ceremonials album are classified as indie pop or baroque pop songs. Those are pop variants that belong to the collective genre known as pop music. Like I said, she is an indie rock and pop artist.

Then what classifies as alternative?

The term "alternative" much like "Indie" and "pop" are more umbrella terms that describe something. Saying a song is a pop song doesn't really completely describe it seeing as how songs like Born in the USA, I Feel Love, Frozen, Toxic, and Yesterday are all Pop songs. The same goes for Alternative and Indie. They sorta describe something, but they are not complete genres, more umbrella terms that people use.

All of them are pop except maybe Azealia and Lana.

Azealia is mainly a rapper.

Lana is??? IDK... her music is so diversed. She ranges from country, blues, Indie in her Lizzy Grant days to Sadcore, Hollywood pop and there are songs that borrows hip hop elements (Diet Mnt Dew & National Anthem), Dance (Ride or Die), and there is song like Million Dollar Man that is Jazzy.

All of them are except for Florence and Azealia. Florence is alternative/indie while Azealia is rap.
Just because Azealia raps over house beats does not mean she is even close to pop.
And I never understand how people call Florence pop. The closest she is would be indie pop.

The rest, however, are pop artists with outside influences. But their main genre is pop.