A joint sponsor needs more than to provide evidence of intention to re-establish domicile. They must show they ARE domiciled. The petitioner has already provided evidence of citizenship, but the joint sponsor does that with the affidavit.
Details matter.
Not actually false. Your statement above IS false. Truth is that neither the petitioner or joint sponsor need to "submit" three years of tax returns. They both need to provide INFORMATION FROM three tax returns and submit only the latest. Further, the joint sponsor has MORE required supporting documentation than the petitioner, in that they must document their status in the USA and that they currently reside in the USA.
1 Yes
2 Tell them the truth about the business trip. That is your primary purpose. You are no more obligated to mention a wedding (even yours) will be one item on your agenda, any more than you are required to mention you will visit a public library. There's nothing wrong with marrying and leaving, but it is not necessary to mention either.