1.No matter what kind of friend you make, I still love you.
2.No matter what kinds of friend you make, I still love you.
3.No matter what kind of friends you make, I still love you.
4.No matter what kinds of friends you make, I still love you.
5.No matter what friend you make, I still love you.
6.No matter what friends you make, I still love you.
What sentences are correct? What is the rule? If more than one sentences are correct, what is the difference in meaning btw them?
They are all basically correct.
The difference depends on who many different kinds of friend, and the number of each kind.
Are you referring to
(1) one friend of one kind,
or (2) one friend each of different kinds,
or (3) many friends of one kind
or (4) many different friends of different kinds
If you have 5 friends, each of the five friends is a different type (i.e., 5 different types).
(5) sounds like it’s referring to a specific type of friend, possibly even to one single new friend who has been criticized as being a bad choice as a friend.
(6) refers to any types of friends
.