Maybe the OP's talking about metrics, and what goes into measuring/computing them?
Just something off the top of my head. If that's what the OP's going for, "startup mathematics" wouldn't exactly be the best term to throw around, looking for clues.
No, not always. It's something a lot of startups misuse. But I wouldn't say that's how everybody does it. I know some startups that offer equity with a slight pay cut, just to gauge your motivation, and bump up your pay soon after.
Honestly, I'd say go for it, open-source it. Like you said, a successful app's more than just changing icons and the like!
One tip - maybe you could think about constructing a tutorial of sorts around your app's codebase? Something like this: https://mackenziechild.me/12-in-12/
Leave the political dimensions aside; any place is as risky.
Personally, I'd love a scenario where a startup helps me out in terms of travel costs, and maybe putting me up for a week while I find accommodation. Not very picky about vacation days much, but having a day or two off every month works, for now. The salary part's a little more complicated - it should take my current pay package into account, as well as extrapolate for currency differences, and consider the cost of living too. It's not a bomb, but it makes a huge difference knowing that you won't really go broke all of a sudden, in a foreign land.
In your case, though - relocation's not a great idea because it can get pretty tricky for both the candidates and you - if their families aren't adjusting to their new surroundings much, it'll affect the candidates, and thus, affect you in turn. I'd suggest exploring every option to make a remote-working scenario possible, and only using relocation as a last resort.
Well, if you ignore general trends and the availability of people for a specific stack, I suppose you could go ahead and write your app in a language like Haskell, or even languages like Rust. But if you want to choose a language that is "meant" for the web and it's something everybody knows, I'd blindly pick Javascript if I were you. Of course, it's not the best language for mobile, but frameworks like Ionic are changing that.
I think Glacier works on very different principles, for very different scenarios. Dropbox, Drive...they're more for everyday usage. Glacier's more for archived storage, where you're looking at a platform to store historical files, that aren't used everyday, but you never know when you might need them. IMO, I'm not entirely sure it's accurate to compare it with Dropbox, in these terms.
I'm pretty sure there's a scarier part where there are still InfoSec pros out there who haven't bothered patching their OpenSSL implementation, months after Heartbleed went public.
I doubt it'll hurt the OP to ask out here, along with consulting a lawyer. IMHO, if you could simply remove the hooks between the company's Github repo and your personal account, you don't need to share your account details.
Well, I've gone with Percona to power an ecommerce site I'm responsible for. Definitely faster than a vanilla MySQL installation. So they use XtraDB on top of InnoDB for greater performance, and so far, it's been going good.
And about its usage being lower than that of CoffeeScript - I'm afraid I can't say much about that, but again - it just hasn't caught on yet. My startup was one of the first to use Docker in production when it first came out a year ago, and now, Docker's the biggest thing ever. So yeah..
While I personally haven't used TypeScript, I can say this - worry not, about its roots. The whole code's open sourced on Codeplex, and Microsoft's commitments to open source are growing. Plus, it was personally overseen by Anders Heiljsberg - the guy's a freaking genius when it comes to language design. The only thing I have against TypeScript is the syntax - personally, I prefer CoffeeScript, due to its Ruby-esque syntax, but that's just me. So if TypeScript's being favored by peeps at your company, go for it!
I wonder what makes the OP believe Python's a "hobby language".
On an unrelated note, I use Python for computational math, and after languages like MATLAB, it's probably one of the most powerful languages one could ever use.
Just something off the top of my head. If that's what the OP's going for, "startup mathematics" wouldn't exactly be the best term to throw around, looking for clues.