If is safe to shampoo daily, as long as you are not using a weekly clarifier that will strip your hair. I wouldn't recommend much more than this but unless your hair is extremely fragile, it will not be hurt from washing it more.
everyday when you shower right after you put shampoo in it
Everyone is different. It depends on how much oil you produce and how long your hair is.
It depends on the individual. People with very dry hair do not need to shampoo as often, while people with very oily hair should shampoo more often.
Every other day
No dye your hair first then shampoo and condition it later.
No that's bad for your hair.
Hydrating shampoo's are often recommended for curly hair, it offers rejuvenating qualities and can be used daily. There are specific shampoo's designed for curly hair containing vitamin B1 which actively hydrates hair. Also useful is frizz easing shampoo's as this can often be a problem associated with curly hair. A number of other hair treatments are available, some leave in conditioners are recommended as great products to try by the curly hair community.
The first thing you should think about is your scalp. Is it greasy, normal or dry. This is because this is where the hair is nourished from and once your scalp is in good condition your hair will be too. Then you can think about your hair; whether it is fine, normal or greasy. For fine hair you can get a volumising shampoo to get some life into if you would like that.
Unhealthy... no. It can however pull natural oils from your hair that are desired in nourished and healthy looking hair. If you shampoo daily, you should also condition daily to avoid a dry damaged looking head of hair. So: this is perfectly healthy!
not necessarily, but the shampoo does dry your hair out, if you even shampoo your hair every other day the natural oil's from your hair can help condition it and make it softer
Once a day for sure with a special shampoo expressly for oily hair.
Relaxers should not make your hair fall out if applied properly. Relaxing your hair should be a quick process and only applied to your new growth. After applying your relaxer you should proceed to shampoo your hair using a neutralizer that will lock your hair into it's straight shape. (Repeat until the water runs clear and your shampoo has no pink color to it. Condition your hair and make sure to keep your scalp moisturized.