I am also a bit fuzzy on the requirements as the data doesn't appear to exercise all of the limits. But it appears that the data can be sorted in some order and then a filter (grep) operation run to select which lines are of relevance. See attached code.

If I don't have it exactly right, I think you will be able to modify this pattern to do what you want. I'm not quite sure about the relationship between col 1 and col 2. The example data had only "matching sets" of those two columns. matching up the lowest col 5 with highest col 7 is accomplished by reversing the sort order of col 7 as shown below.

#!/usr/bin/perl -w
use strict;
use Data::Dump qw(pp);

my @AoA;

while(<DATA>)
{
   my @cols = split;
   push @AoA, [@cols];
}

@AoA = sort{  $a->[1] <=> $b->[1]
                       or
              $a->[0]  cmp $b->[0]
                       or
              $a->[4] <=> $b->[4]
                       or
               $b->[6] <=> $a->[6]
            }@AoA;
            
pp \@AoA;            
=prints

[
  ["xhahhxha", 60, 3, "shdgehsh", 8, 1, 150],      #this one
  ["xhahhxha", 60, 3, "jrthtahtat", 8, 1, 110],
  ["xhahhxha", 60, 3, "hahaghagah", 10, 1, 101],
  ["hsghtahs", 100, 19, "shdgehsh", 10, 20, 400],  #this one
  ["hsghtahs", 100, 19, "jrthtahtat", 10, 20, 300],
  ["hsghtahs", 100, 19, "hahaghagah", 10, 20, 200],
]
=cut
my %seen;
@AoA = grep{!$seen{"$_->[1]"."$_->[0]"}++}@AoA; #first of new col1,2 c
+ombo
pp \@AoA;

=prints
[
  ["xhahhxha", 60, 3, "shdgehsh", 8, 1, 150],
  ["hsghtahs", 100, 19, "shdgehsh", 10, 20, 400],
]

=cut

__DATA__
xhahhxha    60    3    hahaghagah    10     1    101
xhahhxha    60    3    jrthtahtat    8      1    110
xhahhxha    60    3    shdgehsh       8     1    150
hsghtahs    100    19    hahaghagah    10    20    200
hsghtahs    100    19    jrthtahtat    10    20    300
hsghtahs    100    19    shdgehsh    10    20    400
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