LH: Probably a decent chance of compensation for the delayed India-FRA. I'd say very little chance for compensation for the downgrade FRA-US as they'll claim they did you a favour by rebooking on another airline at your request.

CO: Don't think you'll have any chance there. They gave you a ticket for miles, if the operating carrier then doesn't deliver it is not CO's fault. But worth a try, you might get lucky and get compensation from both