Sleeper to Cornwall is the one I often see but the rest is all electric for the Paddington bit - of course trains going West switch to diesel once they get off the electrified line e.g. at Swindon for Cheltenham
2. Don't cars still pollute, even under the low emission standards?
3. Car pollution is also part of business. Do you mean industrial production activity? Fossil fuel burning for heating?
This also makes it possible to build bi-modal trains that run on Diesel on non-electrified tracks and use a pantograph on electrified bits (like London). That's what is being done in the UK now under the Intercity Express programme in order to replace the old Diesel trains (HST/Class 125): https://www.hitachi-rail.com/products/rolling_stock/bi_mode/... - these are the class 800/801/802 trains mentioned by vertex-four in a sibling comment.
I regularly get the Cheltenham to Paddington train, and apart from the slight extra delay at Swindon while they switch power haven't had any problems with them.
Some of the early seat covers are being replaced because they don't wear well though
Dragging trains into/out of London with an electric loco would pretty much kill the frequency of the lines. This isn't the US where we might get five long-distance passenger trains a day - London King's Cross and Euston are busy, with service patterns at breaking point as it is. There's nowhere outside the city where trains could stop and wait for a locomotive, anyway.
Only if it's a diesel/electric, but then you're not really turning off the engine.