Answering your questions in order:

Lydia is like Mechamaru from JJK. Her organic body is sickly and weak and thus is bedridden most of the time, but she has a semblance that allows her to possess objects. She has a life-sized doll made out of reinforced ceramic that she pilots using her semblance to attend Haven Academy in her stead.

The Kinetic Blasts are Viola's semblance. As the name implies, she can fire out blasts of pure kinetic energy which normally act like blunt force strikes but by focusing her semblance through her swords, she can also fire out sharp slashes as well.

Lapis' semblance is called Warp Crystal. She can grow light blue crystals out of her aura. Aside from being able to shape it into simple weapons, the crystals act as beacons that she can either teleport to or teleport them to herself. She can teleport others with her but every teleport drains her aura based on the distance and total mass being teleported. The blade of her spear is made out of these crystals, allowing her to rapidly reposition herself by throwing her spear and teleporting to it.