[2020] Is it normal for a Kalista to move like that? (Also I know I'm bad bare with me)

Yup! Kalista's passive allows her to do a hop in between every auto attack if she issues a move command (right click the ground) once she has started an auto attack.

From the wiki:

Makes her 📷 dash in the target direction after issuing a movement command during a wind-up or right after casting 📷 Pierce.

• The distance scales with her boots tier. The wind-up while dashing is only reduced by 0.66% per 📷 1% bonus attack speed.