It should not have any impact on either of those applications.

Probably they are getting your I-751 file, or perhaps they are going to be forced to admit the file is lost. They may reschedule you, they may...

They were admitted for six months. Staying that long however could have future consequences.

It should not have any impact, assuming CIS approves the application.

Check your travel history and it may indicate your date of departure.

You do not need to do that. Your income can be included in the I-864 itself.

You need to file an immigrant visa petition for the children and they can immigrate to the U.S. and they may be derivative US citizens once they...

Perhaps you could send another letter to CIS that will arrive before the one you sent yesterday and in which you disavow the one you sent yesterday.

It means you must go to USCIS and sign the form I-485.

You are not permitted to work for the first employer, starting on the date CIS approves your new H1b.