Article a(an)/the

1. Give me a book to read.
2. The book I am reading is very interesting.
3. Water is necessary for life.
4. Cotton is grown in the south.
5. I like a strong tea.
6. The tea is too strong.
7. I see the child playing in the garden.

8. "A child playing in the garden is my son." - This means that there are many children playing in the garden, of which only one is your son.

"The child playing in the garden is my son." - This means that there is only one child (your son) in the garden. I suspect this is what you mean, but what you wrote isn't incorrect.

It's hard to correct things like this, because using the wrong article usually changes the meaning of a sentence without making it incorrect. For example, both "I see the child playing in the garden" and "I see a child playing in the garden" are correct, but it's hard to tell which one you meant without context. It's the same for most of your sentences.

Otherwise, all your sentences are perfectly correct.