No this should not impact your wife’s GC status.

Unfortunately this is not a right and will not be produced by USCIS.

While not required it may assist but more information is needed about merits about possible application.

Can a father-in-law fill out an I-864 form instead of spouse?

You may use a cosignor but you must file the I864 as petitioner regardless.

Yes providing a printout of the Zillow information will likely be sufficient.

This is likely for your EAD tied to your I360 application.

No this does not impact future citizenship eligibility.

There is no limit or regulation regarding sending money legally overseas.

How long can I stay out of the United States while I have a green card, in order to get citizenship?

You should be in the US continuously for more than half of the year.

How long will it take me to get marriage based green card after marying green card holder ?

It will take about 2 years for the visa through marriage to LPR.