Can I have a question mark in my paper's title? For an example: "Advertising Strategy: Harmful to the Community?"
It depends on the class, and anyway I wouldn't recommend it.
A good academic paper is one that takes an audacious stand one way or another, even an arguable one that another writer could pick apart. The example you cite just asks a question, which is the mark of an inadequate academic paper. A great title makes a reader want to read the paper, and the question mark serves to dilute this urge.
Debate titles seldom are phrased as questions. This one might be phrased as "Resolved: This Advertising Strategy is Harmful to the Community."