Maya, if you want to shampoo everyday, or need to do an "emergency" shampoo to erase a bad hair day, you can use baby shampoo. I used to use that when my hair was longer, it doesn't contain any harsh chemicals and it isn't drying, either. Plus, it's super cheap. I just bought the Johnson and Johnson brand at the grocery store.
I second putting the product in back first. Something that worked for me was to rub it through my hands so it was evenly distributed, then just lightly scrunch it into the back and work my way forward. Also, I would recommend using slightly more product, and apply it to your hair when it is very wet (before you towel dry it, even). When it air dries, it will be slightly crunchy, but you can then carefully turn your head over and "scrunch out the crunch" with your hands. If you just gently scrunch your hair, it will break up the crunchiness a little.
There's a lot of conflicting information about curly hair out there. I think it's just that something different works for everybody and it takes some experimenting to figure out what works for you personally. It's good that you seem to have some patience and an open mind to try different things.
I love your new cut!