1 and 3 are fine, but 2 isn't really natural because "pretext" is quite formal and "cut school" is very informal.

Yes, I think they are. "Cut" in this sense is a bit old-fashioned for me. I suppose as well a slightly more natural way to say it might be to begin the sentences with "stop always using..." There is a slightly different implication that way as well: "Don't always use" would imply "you should sometimes use a sprained ankle (for example) as a pretext for not going to school", whereas "stop always using..." would imply that the listener shouldn't be trying to get out of school at all. Tone of voice is important for this one though.

The sentences sound like an accusation, and would better be stated as such: You always use a headache as a pretext ... for cutting school! ... for skipping school! These expressions are common in the U.S., as is "playing hooky".