Is it possible to be notified when someone makes a comment under a deceased classmate? I forsee this as a possible problem because someone could make a false remark and I would not know about it.

Not at the moment, but In Memory Subscriptions is something we have on the Task List, so you will be able to do this in the future.

Only Classmates can post In Memory comments of course. Although anything is possible, I will say I haven't heard of even 1 single inappropriate In Memory comment being posted by a Classmate in our entire history. So, hopefully that won't happen before we get In Memory subscriptions in place..