What does a little frown with a dot above a note mean? For example, above the first and third half notes in this famous piece.
It’s called a fermata, and it means to hold the note out longer. In an orchestral piece like Beethoven’s 5th, the ensemble would hold the note until the conductor cuts off.
That’s a fermata. It means to hold the note (or rest) beyond its indicated length. How long? That’s to be determined by the performer. Usually, around 1 1/2 to 2 times indicated note length is a good place to start.
Interesting that you would describe a fermata that way. I doubt if Beethoven thought of it as a smiley. 
Da da da dum…
There’s a T-shirt that says, “I’m a fermata–hold me.”
Cutesy, yes, but nevertheless adorable.
I could be wrong, but I believe I’ve seen it the other way around, under a note. Still a fermata, but then it’s a “smiley with a dot over it, placed under a note”
You’ll get this only occasionally. The ‘default’ is over the note - the most common occurence underneath is when there’s two separate lines of music on one stave.