I've never once had a VC even ask about my paycheck let alone suggest I don't take one. FWIW the second you run a company you literally have to pay yourself at least minimum age, it's illegal not to. edit: Hm, apparently you can take a literal $0 paycheck. Regardless, it'd be absurd for a VC to tell you to do this imo.
This clearly isn't true for eg a single-member LLC, and likely not true in general.
If you're raising VC money then I assume you're not an LLC. But I think you're right that the owner can take a $0 salary.
It's not true, as the founder of the company, you aren't even technically employed (unless you become a legal employee), so there is no concept of wage at all, only dividends and buying stuff directly with the company (fine within reasonable limits).
I feel like I was an employee, I don't really recall the details when I spun up my C-Corp tbh. It does seem that a CEO can take a $0 salary.