Fallen Heroes

Yes. They aren't seasonal units, so they are able to be summoned on banners.

Yup I got a fallen celica on the genealogy banner,so you can if your lucky with pitybreakers.

Yes they can, they're part of the normal summoning pool. The only banners they will not appear in is the legendary banners unless they are featured in it as one of the 8 bonus heroes alongside 4 random legendary heroes that correspond to the color.

Yup. Grima pity broke me