which one is correct 2 ?

I suggested what they should do when facing the same problem again.--correct, the latter part of the sentence is a phrase.

I suggested what they should do when they faced the same problem again.--wrong because the suggestion is for future use and is a suggestion for general reference. It is not a fact happened in the past. Don't be confused by the myth that only tenses of the same group could be used in one sentence. MEANING is very important. However, for reported speech, we may choose either to change the tense of the reported part or not when it refers to something that is generallly true. For example. "You should ask your teacher when you face the same problem again," said Mr Wong. Then the reported speech may be "Mr Wong suggested that we should ask our teacher when we face(d) the same problem again." The verb "should" needs not be changed. More examples for reported speech of something that is still true. He said that his name is/was John. She said that she is/was a girl. He told his students that the sun always rises/rose in the East.

I suggested what they should do when they face the same problem again.--correct. As the suggestion is for future use as a general reference, it should be in simple present tense. The difference between this one and the first one is using a phrase or a clause in the latter half of the sentence.

Here are my opinion:
I suggested what they should do when facing the same problem again.--Correct and simple
I suggested what they should do when they faced the same problem again.--Correct
I suggested what they should do when the face the same problem again.--incorrect

yes, I agreed with you, it should be the first one: "I suggested what they should do when facing the same problem again"