Yes and yes.

If the files are small, the easiest way to "back up" is to read the whole thing into memory. Something like this:

# Loop over all files with a .log suffix
foreach my $fn (<*.log>)
{
    # Open the file, if possible, and read it all into @f
    open I, $fn or warn("Couldn't open $fn: $!"), next;
    my @f = <I>;
    close I;
    
    # Go through it a line at a time
    for (my $i = 0; $i < @f; $i++)
    {
        # If you find "hello" anywhere in the line,
        # Back up two lines and print if possible
        if ($f[$i] =~ /hello/)
        {
            print $f[$i-2] if $i > 1;
            print $f[$i-1] if $i > 0;
            print $f[$i];
        }
        # Note, if you don't care about "undefined value"
        # warnings, print the three elements without any
        # condition.
    }
}
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If the files are large, this could eat up lots of memory. In that case, you'll have to play games with backing up inside the file, which is trickier. (An exercise for the reader. ;-)

HTH