Learn English – Why do we use “a” in front of “unique” instead of “the”

You are right that it gets a little confusing with things like mountains, rivers, etc.

I was going to type up some examples, but this site does it just fine. To summarize it (including only ones relevant to this question):

without "the"

• names of countries in the singular; summits of mountains; continents; towns
• single islands
• parks; lakes

With "the"

• names of countries in the plural; mountain ranges; regions
• groups of islands
• name with of-phrase (ex: The Statue of Liberty); oceans; seas; rivers

I wish I could give you an easy rule to follow with this... but I cant. Some things just work one way, and others a different way. Maybe an expert could explain why the distinction was made. I guess, eventually, you just develop an ear for it. Until then, you may have to just memorize the common examples, and try to use that to "guess" for the other ones.

It's a and not the because the phrase is part of an attributive clause describing scammers. Here, looking to make a quick buck off the tragic death of a beloved entertainer tells us what type of people the scammers are. It's very likely that, to them, the important bit is that this person is someone famous, not that it's Robin Williams specifically. They would be glad to use this ploy to make a quick buck off the tragic death of any celebrity who had died. Thus, the precise identity of the deceased (which is what using the would mean) is incidental; any beloved entertainer would do, hence a rather than the.

The case of MJ, the pop singer is different because the pop singer is an appositive clause serving to identify a particular, unique Michael Jackson among the various famous ones. If instead pop singer were being used to qualify rather than determine MJ (if he were much less famous and the reader needed some additional context to know who he was, say), then using a would be appropriate, and it would tell the reader a bit more about him. For example, consider this conversation:

Alice: I ran into Michael Jackson yesterday.
Bob: I have no idea who that is.
Alice: He's a pop singer.
Charlie: Who did Alice meet?
Bob: Michael Jackson, a pop singer.