Part 1:
Your problem may be that you've escaped the wrong parens: ¹

my($first, $second, $third) = $text =~ /(\([a-z]*\))(?:\s|_|$)/gi;
print "$first and $second and $third\n";
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Part2:

no warnings 'uninitialized';
my $count = $text =~ s/(\([a-z]*\))(?:\s|_|$)/$1$2/gi;
print $count;
use warnings;
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output, parts 1 and 2:

(network) and (test) and (ifcfg)
3
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Part 3:
I'm not at all sure I understand what you want. Please clarify whether you're talking about multiple copies of a parenthesized word or simply "more than 3 parenthesized words in your string."

Update: Oops, meant to say but forgot to write it down, split to an array would also be a valid approach -- perhaps better than above.
Also, though I haven't worked it out, it seems that tr/// might also represent a possibility.

Update2: Adding note ¹ -- or the problem may be that I read the OP as seeking to capture the encasing parentheses... which may be true, but is *not* specifically asserted. ...and if 'untrue,' apologies for the initial observation.