In usual one-dimension search matches can not overlap if we use /g modifier and do not change pos(), but here I'm changing pos() and matches can overlap.

Since you said "In usual one-dimension search", I suppose you may already know how to make it possible for matches to overlap without changing pos. It is done by using look-around assertions.

perl -E 'say scalar (() = "banana" =~ /(?=ana)/g)' will print 2 (because the (?=) portion makes sures there's a match at that position, but perl moves at least one char forward after a zero width match). And you can still get the content of the matches by adding captures inside the look-ahead assertion. perl -E 'say join ", ", "banana" =~ /(?=(ana))/g'.

In the similar node you gave a link to, the main difficulty came from the fact that the lines where not of equal size, but since yours are, your problem translates pretty well to a one-dimension regex:

use v5.14;
my $pattern = qr/#.{10}#.{13}#\./ms;
$_ = <<STRING;
#..#.....#.
..#...##...
.#....#..##
#..#....#..
..#...#..#.
.......#.#.
...........

STRING

say pos while /(?=$pattern)/g;
__DATA__
14
19
25
[download]

Now you can find the row and column of the matches by using modulos and division.

This, of course, only works when the lines are of constant length, but actually, you can just reformat the input string:

use v5.14;

my $length = 20; # Must be higher than the length of the longest line

# Add padding so that each line is $length chars long
# Without checking what char there are (ie, the \n are kept)
# So we know that if a char A is in position $a, the char B below it w
+ill be in position
# $a+$length, or there will be A.{$length-1}B 
$_ = pack "(A$length)*", <DATA>;

# $length - 2 is one line down, one char to the left
my $l1 = $length-2;

# $length + 1 is one line down, one char to the right
my $l2 = $length+1;

my $pattern = qr/#.{$l1}#.{$l2}#\./s;

# The first row and column have index 0 with this code
say join ", ", 1+int(pos() / $length), 1+(pos() % $length)  while /(?=
+$pattern)/g;
__DATA__
#..#.....#
..#...##
.#....#..##
#..#....#.....#
..#...#..#.##
.......#.#
...........
[download]

1, 2
1, 7
2, 1
[download]