Does M1 ver 18.104.22.168 already includes the PHP 7.2 support patch? I want to know if I still need to install the PHP 7.2 support patch after installing 22.214.171.124.
No version 126.96.36.199 doesn't contain patch for PHP 7.2. You need to install it.
You can see below statement at magento community forum.
Additionally, support for PHP 7.2 will be included as part of the Magento Commerce 188.8.131.52 and Magento Open Source 184.108.40.206 releases, which are currently scheduled for late 2018.
Here is link for your reference.