If your data is as regular as it appears to be, a couple of splits instead of regexes will get the job done. 
#!/usr/bin/perl -w
use strict;

while (<DATA>)
{
   chomp;
   my ($basedir, @dot_names) = split(/\./,$_);
   my $type = (split('/',$basedir))[-1];

   my $school = "null";  
   $school=$dot_names[-2] if (@dot_names >1);
  
   #open the file here and use the variables as prefix for each line
   print "type: $type  school: $school\n";  
}
=prints 
type: abc  school: null
type: def  school: null
type: abc  school: cole
type: abc  school: drew
type: def  school: cole
type: def  school: drew
=cut

__DATA__
/home/test/abc/.date_run_dir
/home/test/def/.date_run_dir
/home/test/abc/.date_file_sent.email@wolverine.cole.edu
/home/test/abc/.date_file_sent.dp3.drew.net
/home/test/def/.date_file_sent.email@wolverine.cole.edu
/home/test/def/.date_file_sent.dp3.drew.net

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In reply to Re: Help constructing proper regex to extract values from filenames and concurrently opening those same files to access records by Marshall
in thread Help constructing proper regex to extract values from filenames and concurrently opening those same files to access records by JaeDre619

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