2-3 years for spending $17billion. That may or may not be the case: perhaps it opens for initial production after a mere $2-3 billion has been spent - I’ve no idea - but none of those metrics differ substantially from the kinds of expenditures and timetables Tesla has been demonstrating.
Pretty much spend it all to get the first unit, unless what they're actually doing is building more of a fab complex (many cleanrooms). It's really the cleanroom at the heart of it that defines a fab. Those cleanrooms are getting bigger and bigger which is the primary driver of fab cost. Well - that and the tools that can be 2 stories tall (small - medium sized house isn't a bad mental model for some of them) and need MW+ power supplies - those are expensive too
If they're getting 1 really big cleanroom out of that, then a good mental model is to spend it all to get ready to manufacture the first unit.
It's a lot cheaper if this isn't cutting edge. I.e. 3 or 4 nodes back - 1 and 2 nodes back are still being used for high performance parts. But 3 or 4 nodes back won't work for the training and inference chips we're all so excited about. They would work well for the anti-lock brake controllers and similar though.
The quantity of money between Tesla investment and this Fab network might be comparable - the units though make the economics orders of magnitude different. Units are worth pennies and dollars (some of the big server parts can get into 000s of dollars, but not nearly as many / wafer) for fabs. For Samsung / manufacturer, I believe that what they're actually selling are wafer starts, with the customer 'paying' for the packaging and yield at the end (80% yield means the customer got 80% of the theoretical max from the wafer). I don't know what wafers go for though.
To make the economics work for the manufacturer, you need a LOT of unit volume. So much that Samsung, with all of the semiconductors they consume internally, can't keep their factories sufficiently busy on their own - they need to sell wafer starts to others as well. Of course they've also built a business around making parts for others, so that's an important reason for their network being so large.
The only company I know of that makes and consumes all of its own parts is Intel (within a rounding error). If you want a first order approximation of the size of expenditure and revenue / unit volume to make a fab work (as well as profitability, and making it profitable), look at Intel and it's financials. That isn't $17B for a factory - that's $17B/year for factories, upgrades to the factories, and another similar amount for R&D on fab technology. I'm pretty sure that most of that is the tools in the factory - not the building and cleanrooms themselves. Tesla could cut back on that - maybe 1/2 of each, but maybe not. Like car manufacturing there is a disproportionate gain in profit as you scale up, as well as a minimum amount to earn as much as you spend.
Tesla wasn't particularly profitable with 1 factory (Fremont). It's becoming wildly profitable with 2, with 2 more on the way expected to make things ridiculous. I doubt the economics would work with a single fab, and probably not with 2 or 3, where 'work' = enough revenue to pay for the capital and R&D.
As a Tesla investor, the case for a fab network that is designed to break even would have a lot of explaining how that benefits the business. And a fab network that can be similarly profitable as the rest of the business would need a lot of explaining about where the unit volume comes from, it's value, and the R&D expenditures Tesla will need to get started and how Tesla is going to make enough of that to stay up with and even push the leading edge of the technology.