Does Ethereum's existence hinge on Solidity? Isn't Solidity just a language that one can compile to the lower-level language actually built into Ethereum?
Solidity is the official language, part of the ethereum project, and pretty much all you get when you look for how to develop eth contracts, unless you specifically exclude mentions of solidity. Then you get Ivy (prototype & for bitcoin not eth) and Pyramid Scheme.
So I'd say yeah, technically not but practically it is.
Not explicitly. Currently, it's the most widest used language for interacting with the VM, but it's not the end development goal. I don't think the entire thing hinges on Solidity, though it's probably the most immediately accessible language. The hype driving the price up seems a bit premature, though.
There are a couple of other languages in development that might improve the ecosystem:
Isn't Serpent an earlier effort that was abandoned in favor of Solidity? There was also the short-lived Mutan, V[iy]per (apparently a work-in-progress) and something called Slang.
Someone told me recently that there's an idea to replace EVM (the lower-level language actually built into Ethereum) with WASM. That would allow people to target it with a variety of existing programming languages, some of which are not clown shoes. If that's possible, it sounds sensible.
You could have other languages that compile code into EVM-executable opcodes, but Solidity is currently the language used by all major players in the Ethereum ecosystem for writing smart contracts. Although there's other options (or new options could be made), it's very unlikely that Solidity will be replaced by any of them any time soon.
The promise of Ethereum was to be a global, decentralize, virtual computer. Without smart contracts, it's just another electronic value exchange platform.
I think one can say that these issues of miner 'optimization' and some of the issues raised in the LeastAuthority audit [1] are architectural, rather than Solidity-specific, and which can only be addressed through defensive transaction design.