Nuclear fuel is generated. Native speakers of Romance languages like to use 'fabricated' because it looks like their own fabriquer, fabricar, fabricare..., but it is a faux ami; there are few - if any ...:-? (in Br Eng, at least - cases where 'fabricate' can be used to refer to a material process. (You 'fabricate a story' when you concoct* a lie. ;-)) (In the IT industry, I heard production plants referred to as FABs (an acronym). I suspect the F may have stood for fabrication. If so, I blame the American love of polysyllabic abstract nouns - like transportation where Br Eng has 'transport', or hospitalization where Br Eng has 'putting in/sending to hospital or ....Am Eng dominates the IT world - I'm ducking and covering here ;-)).
As to 'produce' and 'manufacture', 'produce' is more general. Any sort of manufacturing is a type of production, but there are many forms of production that do not involve manufacture. You can produce some work for your teacher; but manufacture typically happens in a factory.
b
* Look it up! I don't just mean tell a lie. ;-)