Hi,
I also have a shared hosting in hostgator and I can manage how I like my file permissions inside my account, also I also have logs so guess it’s just an excuse from your hosting.
Using an old Php version can have impact in all the php code because some things change and other are deprecated.
Can’t understand why they running a version so old, all this together is causing the problem somewhere.
I advise you to change hosting.
-Rui