I was thinking about tuning my 7 string up a half step, so it's like C Standard, but with an extra F at top. Is this gonna cause any problems? Will I break any strings?
All strings break eventually. You could use a lighter guage if you want. I don't think it'll affect their longevity too severely.
Physically there is no issue with what you are attempting, the only thing I could fore see, is that your chords are going to be a little awkward, but if you are just using power chords, and using the extra high string for a searing solo, then you ought to be perfectly fine. Good luck.