1. No, you make it as part of your response to the letter that the IRS sent - they gave you instructions on where and how to respond, right?
When you dispute (politely) their revised tax assessment, at the end you will also ask for an "abatement" of the penalty and interest, since you showed (presumably just above in your response) that you did not owe the tax that they said you did, and therefore, would ask for an abatement of the penalty and interest as well.
The correct word is "abatement", not waiver - sorry, the right word didn't come to mind earlier.
2. There is no Waiver application, just make the request for the abatement part of your response to the CP501.
3. The IRS normally sends you these letters and asks for your response by a certain date. So long as you make sure that you respond by that date, that is not necessarily the end of the conversation. This is the beginning of a conversation wherein you demonstrate that you don't owe the amount that they said you did.
Did you respond in a timely manner to the CP22A? A phone call does not satisfy as a response unless the phone agent is in an amazingly helpful mood to update your account.
As I noted, in your response to the CP501, you need to note the history, like how you got a CP22A, a phone agent said that the CP22A was in error, then the CP501 came asking for a tax amount that you didn't owe, etc. Lay out your proof that you don't owe that tax, or the penalty and interest. Don't make the agent reading your response have to look up your account - of course, they will, but they will be impressed that your presentation covers all the facts.
The people in the IRS office who sent the letter have the power to make this problem go away, just give them a chance to do it.
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