In their sintered state, these advanced ceramics are extremely hard materials, and machining them requires specialized and expensive machinery, far outside the range of the average hobbyist. Machining them when hard is a very tedious grinding process requiring expensive diamond tooling. Even machining them in their green (unfired) state requires machinery that's been specially adapted to shield it from the abrasive slurry and grit that the machining process generates. I suppose you could build bellows for a normal router or mill and attempt to make a BBQ grill that way, but setting up the kiln to fire them to the high temperatures required could be daunting. Here's an article that talks about a shop that does this sort of thing: How One Shop Machines Advanced Ceramics : Modern Machine Shop You'd need to hit those high tolerances to make functional engines, not so much for the grill.
As for your questions:
1: Here's a supplier for zirconium powder: Zirconium Oxide ZrO2 | AMERICAN ELEMENTS
2: The article above talks about the equipment that's used.
3: There aren't too many machine shops that deal with this stuff. It's a pretty specialized field. Here's a company that does it in California ORTECH CERAMICS - Advanced Ceramic Manufacturer Here's one in PA: Precision Machining Services | CNC Machining Services Company | Ceramic Medical Devices - Kadco Ceramics If you're going to one of these places, you might try to arrange a field trip.
4: Since this is a fairly technical field, you'd probably going to have to take a whole raft of prerequisite engineering and materials science classes to get into a class on advanced ceramics processing, assuming that your local community college offers one. Similarly, any books on the subject (except maybe "Advanced Ceramics Machining for Dummies") are going to be pretty dense as well.
But I don't want to discourage you entirely; lots of people go out and do things that people tell them can't be done. It's not impossible; it's just difficult. f you do manage to set this up in your garage or whatever, please let us know how you managed it, okay?