Solution 1:

a) For the "Connection refused" issue, change dovecot configuration to allow IMAP on the default port 143.

b) For the "dualvar is only available" issue see: https://alexcline.net/2012/02/02/message-dualvar-is-only-available-with-the-xs-version-of-scalarutil-error-in-centos-5/

From dovecot to dovecot rsync will be faster, by a magnitude of 100.

c) For the modules dependencies read http://imapsync.lamiral.info/INSTALL there are the package names to use with yum.

yum install perl-Mail-IMAPClient       # Mail::IMAPClient
yum install "perl(Term::ReadKey)"      # Term::ReadKey
yum install "perl(Authen::NTLM)"       # Authen::NTLM
yum install perl-Data-Uniqid           # Data::Uniqid
yum install perl-File-Copy-Recursive   # File::Copy::Recursive
yum install perl-IO-Tee                # IO::Tee