The C corporation was registered but no shareholders were appointed and no transactions have been made in the tax year. Can we file 1120 with 0 shareholders? (Schedule K)
Yes since a full C Corp is it's own entity and the income/expense reporting and any tax due is the responsibility of the corporation.
If you're thinking of K-1's for shareholders, they apply when you qualify and have made the election to be treated as an S-Corp (IRS Form 2553) and file a Form 1120-S. K1's aren't used for a Form 1120 even though a Schedule K is part of the Form 1120 itself. The K-1's are used to report the proportional net income and select expenses to the shareholders who in turn report them on their individual tax returns. A full C Corp doesn't work like that and so it doesn't issue K-1's to it's shareholders.