In order for a group of words to be a phrase, they have to work together to convey some type of meaning.
1. Testing for the system outstanding
3. Labeling for the equipment missing
are not, in my opinion, phrases.
Without the verb is between system and outstanding or between equioment and missing, it is impossible to know how the other words go together to create a meaning.
1. and 4. are perfectly good sentences.
Student or Learner