Should I receive a 1099R for a direct rollover/distribution from one custodian to another custodian ??

Only if it was a direct rollover to or from a qualified retirement plan (401(a), 401(k), 403(b), 457(b), federal TSP or ESOP).

If you instead did a trustee-to-trustee transfer of a traditional IRA to another traditional IRA or of a Roth IRA to another Roth IRA, the transfer is neither a distribution nor a rollover, is not reportable, and you should receive no Form 1099-R.

Yes, you should receive a 1099-R for an IRA rollover. 

From whom? The former custodian who sent the rollover, or the new custodian who received the rollover?

From the first custodian sending the rollover.