is it grammatically correct to use a phrase like "pay no interest" .. as pay is an action or instruction, then you're told not to?

Yes, it's correct. You will often see this in an advertisement. "Pay no interest for one year."

Pay is a verb, yes. But it is NOT an instruction that you are being told to NOT do. It is a statement. "You will pay no interest" or "You do not have to pay interest". Those extra words are not necessary because the meaning should be clear without them.

When rates are low, it seems banks pay no interest. That's another meaning for the financial world. If you mean, "pay attention" or "notice," it also works for that.

It's acceptable. In some contexts it's poetic, as in "Strew no roses on my grave ... "

No interest is the amount of zero not a negative command. Pay no interest means Pay interest at 0%

Yes, it is grammatical.

Other examples:

Tell no one.

Give no quarter.

Ask not what your country can do for you.

Heed not the rabble who scream, "Revolution!"

Yes.