What you eat has a negligible effect on your skin, however, how you eat can affect it greatly. Take steps to avoid getting any food, especially oily food, on your lips or around your mouth. If you do get a little food on your skin, wipe it off quickly with a tissue or napkin.
Shaving daily in the shower with a cleansing shaving cream or gel (I like Gilette Series Deep Cleansing) is the best advice for males with mild to moderate acne. Be sure to use a razor with one or two blades, as those fancy multi-blade razors irritate the skin and are awful at actually cutting facial hair (it's impossible to apply enough pressure to distribute it evenly among the blades without irritation).
Ice is freezing cold, and thusly, you shouldn't expose any part of your body to it.
I've noticed much of your acne is around your mouth, please do not take this as insult, but you can greatly reduce acne in that area by eating more carefully (literally not getting as much food on your lips, chin, etc.) and avoiding hard alcohol (as alcohol kills cells, causing oil production).
I believe Dan recommends using the CSR cleanser as shaving gel. I've found this to work well, though it can be difficult to wash off fully without a washcloth (something Dan claims is too irritating) if you don't shave in the shower. I've also found Gilette Mach 5 (Clean Skin) and Gilette Series Deep Cleansing gels to be very pleasant, without any adverse effects. Also, make sure you're using a single or dual bladed razor (if you use a disposable cartridge razor), as anything with more blades tends to be extremely irritating and not particularly effective at actually cutting hair.