a) Definitely agree, still that is a good use for the plutonium generator. Also bear in mind that as your vehicle increases in size, the panels and batteries that can fit increase as well. I'm not thinking of a fast, agile, high mileage truck of course.
b) Definitely, but electric power in cata and IRL is too nice to pass up. 99% efficiency, renewable,
easily storable, useful for lots of purposes. Also you don't care about the noise if you are building such bases anyway.
c) I believe you are thinking of engines with nominal power in the GW's if you think they are too large to fit. They'd be large, definitely (~2x2 car tiles sounds reasonable) and weight a couple of tons. But the point would be to use them when nothing else works (diesel and/or diesel-electric train engines would work too, but are still larger)
to a) The problem persists ; Solar panels are just too...bad, at least if you stay within the first 2 tiers of panels/their reinforced variant. They need a lot of time to fill several batteries, and an engine like proposed would eat through batteries like there is no tomorrow. You would definitely need a reactor or a different kind of power source, maybe additional to the solar panels, which you can activate while driving.
to b) Actually, a lot of people would be interested in a mobile base whcih is at least somewhat silent. That does include me ; For example, I'm playing with hordes, and every single noise would mean that I keep getting swarmed by zombies, everywhere. This did happen to me in the past, I drove around in my mobile base with several gas-powered engines, went to sleep, and the next day I was in an ocean of zombies - there were so many in fact that I couldnt even drive the vehicle out. That's why I only use rather silent turrets as well - usually laser turrets and/or flamethrowers and there like. I might have something heavier like a grenade or rocket launcher too, but i only use it manually against big enemies.
to c) I looked around a bit and found measurements like 3mX1.5mX1m ; smaller ones were still around 1.5mX1.5mX1m ; This is, in my book, as big as some small cars, especially if you consider that 1 car-tile is roughly supposed to be roughly around 0.5 metres.
Now you gonna ask me how i came to this measurement. Very well: a normal car in dda is 4x6 tiles big. On average, a car is around 4.5 meters long and 1.9metres wide. This means that we have 0.75m on length and 0.475m on width per tile. If you compare other cars and their tiles you get similar measurements, therefore I usually average it out to about 0.5 metres per tile. One bigger engine might therefore have measurements of 6x3 tiles, while smaller ones would still clock in at 3x3 ; even if we use the high estimate of 0.75 metres per tile we still get 4x2 on the bigger ones.