It's a lot less than that in terms of total personnel costs ($100K is a modest salary-only for a software engineer, it's extremely low as a full cost of employment.)
Sure. But it's probably nowhere close to your salary + benefits + overhead cost to your employer.
On top of whatever your direct employer charges to the government agency hiring them to cover profit and other costs (management overhead, contracting overhead) associated with your employment, there's also contract management overhead for the government agency. For contractors, the total cost is usually a greater multiple of salary + benefits than it is for direct employees (though if the benefits suck enough, maybe still a smaller multiple of bare salary.)
1) 30 top notch engineers to build the MVP and then iterate.
2) 300 engineers - the first 100 to step all over each other trying to build an app and the remaining 200 engineers fixing the bugs from the first 100.