Apply 'glob' to get a list of filenames matching a pattern. From your example file names, I assume you mean "leading 0's". That permits perl's builtin 'sort' to find the largest numbered file name. Then extract the number, add one, and open the new file to write.

use Fcntl qw(:DEFAULT :flock);

my $path = "/path/to/data/";
my $pattern = "[0-9]" x 7;

# Every program which creates a datfile here must honor dat.lock
# take the lock before we read names
my $pathlock = "${path}dat.lock";
open LOCK, "> $pathlock"  or die $!;
flock LOCK, LOCK_EX   or die $!;

my @lastfile = sort glob("${path}${pattern}.dat");
my ($nextnum) = $lastfile[-1] =~ /(\d{7})\.dat$/;
$nextnum += 1;
my $nextname = sprintf "%07d.dat", $nextnum; # answers question 2

open NEWDAT, "> ${path}${nextname}" or die $!;
# ...
close NEWDAT or die $!;
close LOCK or die $!;
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Tested. For compatibility with older Perl, I've avoided the superior 3-arg open and autovivifying lexicals as file handles.

After Compline,
Zaxo