which elliptic curve is going to be used for Casper?
The sharding/Casper proof of concept code uses BN128, and the not-set-in-stone plan is to move to BLS12-381.
which Distributed Key Generation is going to be used for Casper?
We only do plain BLS aggregation (see here); there is no DKG. Aggregate public keys are recomputed for every aggregate signature with cheap curve multiplications.