Rex and Pyra do love each other, obviously – she sacrificed a lot to keep him alive – but it's entirely platonic. They don't split up after the game ends, but their relationship is not one based on passion.

Is Rex and Pyra canon?

Canon. Both Rex and Pyra share the same life force, as Pyra's core was placed in Rex's chest. She acts as a support throughout the series. Both want to reach Elysium, Rex so he can stop wars and ask for enough land so everyone can live in peace, and Pyra for a similar reason.

Does Nia actually love Rex?

Despite it being clear that Rex doesn't have any romantic feelings for Nia, some people make Fanfictions of the two falling in love, once Rex got realizes his romantic feelings. What they both share in common is that they are both orphans and grew up never knowing their family or never having one.