If it's really serious, you can get a politician involved. I recommend the Senior US Senator from your home State. They may not help expedite your case, but they can help arrange a non-immigrant visa so your spouse can accompany or follow you to be your caregiver temporarily.
"Being told" is a notoriously unreliable source.
If your wife wants YOUR family name to appear on her Philippine passport, she will need the RoFD, but it is not needed before filing the I-130. The visa and green card will be issued in the name in that passport at the time of the visa issue. That's about a year and a half to two years from now.
You can file now using the new married name, or just use the new married name from the NVC stage onward. Or change it anytime between when the new passport is in hand and the visa interview.
While I am giving you the correct information, what is required to file the petition is made very clear in the official instructions for the I-130. Download and become an A-Student of them.
1099s are only used when filing a tax return. They are not requested for years a tax return was NOT required. She didn't file taxes the other years because income was below the filing threshold. There's a box to tick that says that right in the section that asks for information from tax returns check it.
Yes, it is a viable plan. Note that actually living in the USA and evidence of that, like a lease and job, are all the domicile evidence needed. One most recent pay stub, will typically be enough, as it will show year to date income.