I have a very dry skin so I only use water to rinse my face daily and a facial scrub once a week. It seems to work fine. Should I start using face cleanser?

I'd say the fact that your skin is very dry means that something is not working perfectly with your routine. I'd opt for a very gentle cleanser once per day, at night (a few options here: https://whatsinmyjar.com/search/cleansers/cleansers-for-sensitive-skin), drop the scrub (it might be making your skin dryness worse), and definitely use a moisturizer 2-3 times per day (plus sunscreen in the AM when going outside).