So when using PHP on the free hosting plan after a certain amount of resources you can no longer use it and it pops up with this default page saying that all of the PHP resources have been used. Is there any way possible that before it gets to this point that all the resources are used that it shuts off the PHP and redirects you to a different page?
Yes, there is. With what you described, I wouldn’t be surprised if you hit the EP limit or the CPU limit.
What you described is temporary, it only lasts around 5 minutes. However, if you continue on that trend of every five minutes hitting the limit, you may be temporarily suspended.
I agree with @wackyblackie, since the entire point of the limit is to punish your website, not allow you the chance to redirect your visitors elsewhere.