Expected:
echo ('string'==0)?"TRUE":"FALSE"; // FALSE - OK

fix your expectations!
'string'==0 evaluates to TRUE

php > echo ('string'==0);
1
php > echo ('string'===0);
php >

that's how PHP works all the time 
https://www.php.net/manual/en/language.types.type-juggling.php

Thank you for taking the time to write to us, but this is not
a bug. Please double-check the documentation available at
http://www.php.net/manual/ and the instructions on how to report
a bug at http://bugs.php.net/how-to-report.php

// You are joking?
// It violates the laws of logic.
$a=0;
$b='string 1';
$с='string 2';

if(($a==$b) && ($a==$c))echo "\$b==\$c";

// But $b don't eq $c.
if($b!=$c)echo "\$b!=\$c";

If decided that this is not an error. That does not equate \0 to any string. Let it always be not equal. Because, it is ambiguity.
Is this logical?

<?php
if("any string"==0)echo "this\n";
if("\0"==0)echo "and this\n";

//Result:
this
end this

Or do you want to say that when comparing with int, any string == 0? If so, then the question is closed. But "8"==8, "0"==0, "7"==7, "7"!=8 but "7"==0

what about reading a php documentation for beginners and start using === instead spam bug trackers?

jesus christ with == one of both needs to be implicit casted before they are compared and a lot of stuff casts to 0 but again: everybody knows that and the documentation is very clear

This happens due to PHP's nature of type juggling. You are supplying a string on the left operand ('string') and comparing it to an integer on the right operand (0). Please refer to the documentation for this:
https://www.php.net/manual/en/language.types.type-juggling.php
https://www.php.net/manual/en/language.operators.comparison.php


If you supply the same type on both operands you will get the expected results:
https://3v4l.org/Zkind

You may also find this RFC proposal for PHP8 by Nikita relevant:
https://wiki.php.net/rfc/string_to_number_comparison