As far as i know that dandruff won't cause eye irritation. But it may contribute to Blepharitis which is a inflammation of the eyelid and surrounding area. Usually, blepharitis is result of bacterial growth. But it can also be associated with dandruff of the scalp. In fact, of you suffer dandruff, you can choose anti-dandruff shampoo to control the condition. Hope this can help you.
It depends. For the most people, dandruff can not cause damages to eyes. But for some people, dandruff can cause eye allergies. As a kind of allergen, dandruff can make your eyes red, itchy, watery, swelling and so on. If your eye irritation is caused by dandruff, seeing a doctor and taking some medicine can help a lot.
Yes, the dandruff can cause damages on eyes because of the invisible bacterium. It will easily cause the irritation. You'd better use the eyes drops to release the eyes symptom. At the same time, your eyes will be moisture. You could use the warm compress to make your eyes feel comfortable.
As a matter of fact, I quite understand your concern for you really care about your eye health. From my perspective, I would say, dandruff would not lead to damages to your eyes unless you directly put dandruff into your eyes, but that is impossible right? And since there is little connections between eyes and dandruff, you just need to take it easy. And try to avoid some other irritation sources to your eyes.