Correct. Many OEM motor manufacturers like Bosch, and vehicle manufacturers like Tesla, Nissan and VW are all either using and or developing induction motors that don't need any rare earth materials. It makes more financial sense to move away from RE PM motors, and switch to induction as they are cheaper to manufacture, and aren't reliant on supplies of rare earth materials from countries with questionable economic and political standpoints.No RE elements in batteries in but are used in electric motors and other parts, though they are developing RE free motors.
Batteries are split into their individual cells which are repurposed when no longer viable for use in a car, but the cells can't yet be recycled routinely, it costs more to recycle than to mine new lithium
There are a growing number of recycling facilities opening up which can recover over 90% of the materials used in EV batteries. The main issue is there are currently very few batteries available to recycle, as they have a very long life, and because of the reuse market, prices of recovered batteries are expensive.
Used EV batteries are valuable as demand is high and supply is limited. Contrary to popular belief, EV batteries won't be going to land fill, as they are just too valuable.