Unfortunately you cannot make changes after the D260 has been submitted. You can notify the consular officer at time of interview.

You may amend this at time of interview without issue.

No this is not advisable as you must establish that you are financially able to remain in US for requested period of time.

Will I have a security check?

This is normal at this time due to regular delays but coupled with Covid related issues of scheduling appointments

Can I travel with just an extension notice I751 without my expired green card since it is lost?

No you should obtain a stamp in your passport prior to travel.

Best to respond to the RFE or withdraw the application.

Yes you can remain in the US with pending extension application filed prior to I94 expiration.

You may begin the process by filing Form I130 with supporting documents and fees.

The sponsor and cosignor must sign the I864 and if household member is I864A.

How can I get my interview without leaving US

You may apply for adjustment of status depending on the category of filing. Best to have an attorney review your case.