Humans can't share ideas directly, they pass through language. Some idea is created at the other end, nominally the same one, but there's no reason to suppose a universal internal format. Even translating between human languages loses details, where words in one language map imperfectly to words in another. Moving ideas directly from one brain to another probably can't happen. So the statement in language doesn't map very well to the idea (whichever person's version of the idea). And at some point before the idea is formed there has to be some sort of proto-idea or potential, with less definite boundaries. So "there is no proper idea" sounds right to me. There's something idiosyncratic, not the formal idea that's frozen when put into words.

That's a really deep question. Obviously there are types of creativity that don't require words, like painting or sculpting, or improvising music, but I'm having real difficulty imagining programming without something at least resembling natural language. The closest my imagination gets is Scratch/Blockly, but even then you're essentially creating an AST composed out of statements and expressions, even if they're pictorial.

Can you imagine the (intentional) creation of a program entirely without language?

Or, I suppose, if you're ok with it not being intentional, you can program via an evolutionary algorithm - is that what you have in mind?