Can an E7 give a counseling statement to a CW4?

Sure, and so can I!

Can any enlisted service member counsel an officer? No. Can they advise the officer? Yes.

If a Navy CPO were to write me a counseling, I would give him/her a written counseling for fraud, waste, and abuse of government resources (pen, paper, and my time). Seriously though, I agree with CWO5 Foreman. If the CWO is that jacked up, it is the E7's responsibility to take the matter up the chain for resolution at the appropriate level.

According to military doctrine, anybody can write up anybody regardless of rank

Is this a serious question?

I've never seen an E7 dumb enough to try it. If they have made SFC that level of stupidity may be out of their lane.

I recently experienced something similar to this in my unit. Do to a medical limitation I was unable to exercise and taped out 1% over. The question was who was going to counsel me. I didn't have any influence in the decision but my commander determined it had to be a higher ranking officer. In this case since I am a field grade mine will come from our XO (Major ). I think this is because you cannot counsel up only down.

Probably if ordered to do so by the Commander if the Commander is too lazy to do it themselves but Uh hopefully just a positive counseling statement

Really? Can a E7 give a counseling statement to a O-4/5? I do know the W4 can give a counseling statement to an E7 though.

Hell no!! If anything it would be the W4 giving the E7 a counseling session not a statement.