Is it a known fact that IM doesn't work with Safari or is it just my situation?
I am root admin.
IM is active if I sign on using Chrome.
No IM box in the lower corner if I sign on using Safari and no Turn on IM in the Member Functions drop down.
Other classmates, but not all, report no Turn on IM option in their drop down lists also, and they are not using Safari, but I don't know if they have checked the IM option in their Profiles.

IM is Flash based. Most Mac devices do not support Flash.

Apple software might not support Flash but Chrome for the Mac does, so it isn't Macs that don't support Flash is just software written for the Mac may or may not support Flash.

This LINK might be useful for some iphone-ipad IOS users

The alternative may be that you closed the window at some point using the X in the corner. If you clear your cache and history, it would reappear ... IF that were the case.