2)Both are correct depending on context. If you want to indicate a specific part of the chicken (i.e. a favorite part) then “which part of the chicken do you like?” is correct. If you allow for multiple answers then “which parts of the chicken do you like?” is correct.

3)The library has different types of books.

4) Both are correct although “the fruit stand sells a variety of fruits” sounds better to me.

You see, these nouns are both count and noncount nouns. This website clarifies the grammar for you:

http://www2.gsu.edu/~wwwesl/egw/nouns/online.htm

2. Which parts of chicken do you like?

3. The library has different types of books on sale.

4.The fruit stand sells a variety of fruits…I think…

because there’s multiple stars

b)at outside, i ask my son, can u count the number of stars in the sky? right

same again – multiple stars

2) which part of chicken do you like? or which parts of chicken do you like?Which sentence is right?

both right – if you only like one part of chicken then first one correct

if you like multiple parts of chicken second correct

library has different types of books -right

multiple types of books

fruit stand sells a variety of fruits – right

multiple types of fruits

The two that might call for singular is the chicken one (are you giving them one part or more than one part?) and the fruit one. Sometimes fruit can be plural. (i.e. “I like to eat fruit.) So grammatically either is correct, but used with the word “variety” I think “fruits” sounds better.

…anytime there is more than one single something you can make it plural.

2 Which parts of chicken do you like?

3 Books

4 fruit ……….collectively it is ‘fruit’…such as saying ….

The salesman sold me differing varieties of fruit.

Fruits would be used like this:

Fruits that I love are nectarines, bananas, and apricots.