Honda Hybrid Technology Explained

Yes, you can get a manual hybrid car, but it will be a mild hybrid. Mild hybrids have manual transmission and can't travel on electric power alone, but the electric motor is simply there to reduce the workload of the petrol engine during acceleration etc for efficiency. 

Full hybrids and plug-in hybrids don't have manual transmissions because the electric motor directly powers the wheels like an EV, bypassing the need for a manual transmission system.

Yes, hybrid cars, as the name implies, use two sources of power – electric and fossil fuel. So, they still have a conventional combustion engine, that runs on traditional fuel, to power the car on longer journeys or higher speeds. This means they either need petrol or diesel.