Yes you may apply for expedited processing although results vary.

Yes this would impact your naturalization application.

It can take over a month for receipt notices.

Yes USCIS may review previously submitted applications for immigration benefit.

You may file a FOIA request for your immigration file.

After marriage you may apply for adjustment of status through your good faith marriage to USC spouse.

Yes you may apply for a tourist visa with a pending petition for permanent resident but be prepared to show eligibility for short term visit.

Yes you may petition for your spouse despite pending case for your mother.

The corrections should not detrimentally impact your application.

You will need to wait until a visa will become available which will take many years. Refer to the visa bulletin for guidance.