Please help. some words about human's body.
I have got some questions about some words of human's body.
1 how many should do a man have ? two or one ? Is there a left shoulder or a right shoulder?
2 Hair is a countable or uncountable noun ? In dictionary it says hair is an uncountable noun. but some times I saw there is a "a" appeared before "hair"
3 Why "toothbrush" ? Not teethbrush. I see that teether anf toother are both acceptable. But when we talk about brush, why don't say teethbrush.
4 We got a thumb, a index finger, a middle finger, a third finger, the little finger on one of our hands. Can we count a thumb as a finger. If no, why people always say we have five fingers, if yes why the third finger called the third finger but not tje fourth finger.
I am recently learning these simple words with my son, but a little confused with these words.
Thank you for your comments in advance.

Question

Please help. some words about human's body.
I have got some questions about some words of human's body.
1 how many should do a man have ? two or one ?  Is there a left shoulder or a right shoulder?
2 Hair is a  countable or uncountable noun ? In dictionary it says hair is an uncountable noun. but some times I saw there is a "a" appeared before "hair"
3 Why "toothbrush" ? Not teethbrush. I see that teether anf toother are both acceptable. But when we talk about brush, why don't say teethbrush.
4 We got a thumb, a index finger, a middle finger, a third finger, the little finger on one of our hands. Can we count a thumb as a finger. If no, why people always say we have five fingers, if yes why the third finger called the third finger but not tje fourth finger.
I am recently learning these simple words with my son, but a little confused with these words. 
Thank you for your comments in advance.

Answer

1 - people have two shoulders. And yes one is the left shoulder on the left side of your body and the other is the right shoulder. 
2 - a hair is a single hair. Hairs is countable (for example: three hairs) and hair is uncountable (the man has a lot of hair on his head)
3 - A toothbrush is used to brush your teeth plural or could be used to brush a single tooth
4 - yes the thumb is a finger. What you refer to as the third finger is called the ring finger and is really the fourth finger.  So from the inside outwards you have the: thumb, index finger, middle finger, ring finger, and little finger (also commonly called the pinky finger in American English)

Hope this helps!

Answer

There’s an old joke about toothbrush/teethbrush:

Q: How do you know that the toothbrush was invented in [insert name of rural, unsophisticated state/province/area]?
A:  Anywhere else, it would have been called a teethbrush.

The joke is that most people from [rural area] have lost all but one of their teeth.

Answer

Darrel's response answers most of your questions.
It seems to me it is all about emphasis. If I want to count fingers on a hand, I just count five. If I want to,  for some reason emphasise the thumb is different, I call it a thumb.
Should I want to contrast the left with the right, I can do so. Otherwise, shuoulders. Be it on your shoulders how you use it.
 I see that teether anf toother are both acceptable.