The boys playing are my friends.这句话对吗?

同意楼上，做主语是不能省who are
或者The playing boys are my friends.
分词做修饰名词时放在前，短语放在后。

有语法错误，应改为The boys who are playing are my friends.

这句话不对应该是
The boys are playing with my friends.

ed 表示被动，或动作已完成；而ing表示主动，或动作进行。

The boys playing are my friends.
是正确的,可以把中间的(who)和（be）动词省略

例如：The little boy standing over there is a classmate of mine.
站在那边的小男孩是我班的同学。

什么时候用ING,什么时候用ed，是要依照你完整的句子中出现的格式。
给你一个复杂一些的例子：
The houses being built are for the teachers.
= The houses（which/that are）being built are for the teachers.
这里没有省略Be动词是应为被动语态

三种时态的:
The problem to be discussed tomorrow is very important.
The problem discussed yesterday is very important.
The problem being discussed now is very important.

强调一下,在省略之后就不是定语从句了,而是非谓语动词作定语.