Yes. But keep in mind that the copyright of any contributions you might get will be held by the author of that contribution, not by you. The contributor might license that contribution under the AGPL only, and thereby put a stop to your little scheme. You would have to either get a license from the contributor to your dual licensing scheme, or simply require all contributors to sign the copyright over to you, which is most commonly done in a so-called Contributor Licensing Agreement (CLA). However, CLAs are rightly disparaged for being unfair, in that it lets you, and only you, profit and monopolize what might become a community effort. A requirement of a CLA will most certainly discourage many, if not most, potential contributors from contributing.

If you're the sole copyright owner, you can offer as many different licenses as you want, and no copyleft license can interfere with that.

That's not how licensing works. If you write the software, you can release it under any license(s) you want. The license states the terms under which you'll let others use the software.

Yes, you can licence it however you want because you are the copyright holder. See mongodb. IANAL. Licences are to restrict those who do not hold copyright.