Option 1: If your sent message folder is "outbox" (I assume you are using Maildir format for mail, so actual path is
~/Maildir/outbox), then you can start
mutt with the command:
mutt -f ~/Maildir/outbox
mutt -f =outbox
= is a shortcut used by
mutt to indicate a subfolder of your Maildir)
Option 2: When viewing inbox, press the
c key. If your
mutt is properly configured you should see a list of folders in your Maildir. Select the folder you want and press Enter.
I don't understand what do you mean by "send a new mail against the first delivered mail"? Do you mean reply to the received mail? If yes, this is done by pressing the
r key on that mail.