How to check Frame No. and/or Engine No. of Mercedes-Benz and BMW cars online ? Please help !?

that depends on which model.

since this is in mercedes-benz section, l will answer that only.

chassis/VIN number can be found on:
*windshield. in the front, driver is side, from outside (just above the wiper blade).
*cross member under the passenger seat (move the seat backward fully, peel up the small floor cover)
*radiator cross member
*rear panel cover (access from the trunk, remove the covering)

engine number:
bell housing (from above, underhood), side of the block (from below)