Yes, it's a good idea to use some type of shaving cream with warm water when shaving in order to avoid irritating the skin and for a smoother shave.
No you can shave without shaving cream, but I don not recomend it. Shaving cream lubricates the skin so that the razor balde glides over it cutting the hair only. Without shaving cream you would...
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No. It would just clog up your razor.
Yes. It helps greatly to reduce irritation.