Do I need to file for an extension if IRS has not processed my manual tax return until April 15th? I had to submit my 2018 return by mail due to change in family status.

No, you do not have to file an extension if you mailed your return to the IRS.  Your return is considered received by the IRS when you put it in the mail.  It does not matter when they receive it or process it.  It just has to be postmarked by April 15, 2019.