Yes you should indicate your marital status as married.

You should amend the filing to indicate your correct marital status.

You can refer to the I134 here: https://www.uscis.gov/i-134

No this should not result in rejection of application.

No separation is not required in this instance.

No this will not be a problem as long as disclosed at interview.

You will likely be denied due to extensive travel outside of the US.

It depends in the US consulate but likely many months.

You will be rescheduled for second interview.

Best to wait to travel until after decision is made.