and there are a few related issues, you can keep an eye on them.
About the date, please check the timezone setting for your CLI (command-line) PHP. This is what cron is using, so the notifications will get the timezone setting from it. Note that this is different from the setting you have inside SuiteCRM, and in your web server’s php.ini.
You mentioned you had a “server administrator”, I hope he knows how to enter commands?
You should be able to access your shared hosting via SSH, that’s where you enter commands. If your shared hosting doesn’t allow SSH access (or another equivalent shell access) then I would say you need to consider changing your hosting. I don’t think it’s a good idea to try and run a CRM without being able to reach your OS.
There are many shared hostings out there with SSH access (limited to your area of course, but enough to work with). I really cannot recommend trying to use SuiteCRM without some decent administrative access.
SuiteCRM is a complex, multi-layered app that writes itself when you customize it. It has inevitable demands for Administrative care, things like file permissions and CLI PHP access, which are not very complicated, but if your hosting is too restrictive, then it is not adequate for SuiteCRM.
If you don’t have access to the CLI php.ini, which is the one used by scripts launched by crontab, which is what the Scheduler Jobs use (for example, meeting invitations), then sorry, you can’t set the timezone.
The CRM script is emphatically not buggy in this regard. This is the way Linux works, and the way PHP works. There are two different php.ini’s, one for the web app, the other from command-line (CLI), and there is no way that the web app can change a setting for the CLI.