SQL Strict mode will not be disabled. Contact the script vendor to see if there is an option with strict mode enabled. Otherwise this script will not be able to be used with the hosting.
In response to the Cloudflare part of your question, no. The free sub domains can not be used with Cloudflare, only exception being those who had it setup with cPanel prior to server migration.
You must post your request at that link as the error message instructs. That is the only way it will be reviewed.
https://community.x10hosting.com/threads/multi-account-unblock-requests.209963/
Gmail is likely rejecting it due to it being unauthenticated mail by just using mail().
It would take a lot to get it to accomplish that task, but I would recommend using a library like PHPMailer
This error code is invalid. Trying again and getting a new error code wipes out the previous one. Please try again. If you get a new error code, please post that error code and refrain from doing anything after that so the code stays.
This mean that content on your account was found to violate the Terms of Service and/or Acceptable Use Policy.
Please wait for staff to review to confirm.