1. You can't pump the output from a combi, so no, you can't fit a pump.
2. Assuming the pressure and flow rates are adequate you should be able to run a mixer shower off the combi with no difficulty and shouldn't need a pump anyway.
3. You will obviously need to run a hot feed to the mixer, as previously you would only have had a cold supply to the electric shower.
4. The cold supply will be at mains pressure as will (to all intents and purposes) the new hot feed from the combi.