All fair questions. I'm no expert but have been involved in engineering a couple mules/prototypes. Generally in earlier stages of development ("alpha"), you have prototypes that focus on either tech/engineering or aesthetics/ergonomics. Later-stage mules will combine both of these domains. 

The former are generally existing production cars cut up and retrofitted with custom parts. I'm a chassis engineer, so in my domain, you'll have a cut-up production car with custom suspension parts and chassis/unibody modifications. Depending on what you are trying to test/validate, brakes and springs/dampers may also be custom prototypes. Custom parts are machined, fabricated, or modified production parts, but usually not cast for instance. I would never want to own any former mules lol, but they are neat to work on and test with. 

Very early stage aesthetic/ergonomic prototypes often don't have suspension or powertrains at all. The ones that do will use as many off-the-shelf parts as possible for obvious reasons, usually built around a one-off unibody, even if the basic architecture isn't production-representative.

In a lot of ways it's not too dissimilar from how people build their own custom cars, just with a lot more money and engineering depth. I wish I could get into specifics because I've seen some really cool stuff, but it's also all very secretive, which is a big reason why you don't often see documentaries or the like. Sometimes stuff gets tested that doesn't make it to production and companies would rather not share that information. Even internally, only a very limited number of people are exposed to these mules, particularly ones that are representative of the design concept to avoid leaked pics of future products.