Wiring – Can i use 3 wire for service installation

Yes, you can add an insulated ground bar in the can (you should be able to get one specifically designed for your particular can, but here's what they look like):

.. and then connect it to the other ground bar using a piece of #4 AWG (solid bare copper, or stranded THHN insulated) assuming you're still at 200 amps. This guarantees that the green bonding screw that's actually bonding your neutral on the other bar will affect both bars if it is removed. It's common to add these for isolated grounds, where they're connected to a different ground altogether instead of the other bar.

Note - the one you buy may come with its own bonding screw, and the appropriate tapped hole to receive it - so check for that prior to connecting the two together (IOW, read the installation notes that came with it).

To meet current NEC codes you cannot have neutral and ground share the same grounding rod. Ground requires its own separate rod from each panel and sub-panel installed in the house.

The depth of the rod outside depends heavily on your area as factors like precipitation, soil composition and climate affect just how far the rod needs to be placed into the ground. Performing this work likely requires that you obtain a permit from your local municipality, meaning that you will need to have an inspection anyway. I would ask the inspector what he will be looking for in a ground rod.