Are there any penalties or notices for a player who frivolously reports other players?
Do they ever get at least a notice saying “Hey, you are frivolously reporting other people, we (referring to the Blizzard employees who monitor reports) would like to inform you that you are doing this.” Anything along those lines?
If they report someone and that someone has not broken the rules then nothing happens. If that someone has broken the rules then Blizzard takes action.
You can report someone for anything doesn’t mean they need to get actioned for reporting. Blizzard may educate them by linking the rules so they know in the future that whatever they reported was not actionable though.
Oh and the answer is no there are no frivolous reports.
If you’re repeatedly reporting a player as a harassment vector, yes, you could have your wrist slapped, so to speak. I seem to recall that the first response would be a message from Blizzard telling you to knock it off.
So the person who is reporting gets to report someone and forget about it in 5 minutes and the person who got reported has to cross their fingers and hope that the Blizzard employee will take their side?
So there is no reason not to report anyone for anything ever?
There’s nothing stopping someone from sitting in trade chat and reporting anyone who says anything in trade chat (or general chat) to anyone?
Does the person who got reported have any way to defend him or herself?
Nope, not a thing - other than that would be an incredibly boring thing to do.
If you’ve broken no rules, you have nothing to worry about and won’t even know you’ve been reported.
You will never actually know you’ve been reported. Unless Blizzard actions your account for a violation. A report doesn’t automatically means a penalty.
There’s no ‘taking sides’. If someone is reported, the report is investigated, and if rules were broken, they’re sanctioned. If they’ve done nothing wrong, it ends there, and the player never even knows they were reported.
Stop listening to the people who say " /reported!".
Better yet, if they say “/reported!” report them for spam, which is what that is.
I don’t know if I’d qualify that as spam. Nonsense more often than not, but probably not something to be report as spam. 
Yeah, that isn’t spam lol
It would probably depend on how often they type it. I’ve seen “reported” spammed like “Thunderfury” in chat.
I have seen people say reported the reporter for reporting, and on an one. It becomes comical.
Ok thank you for the input/advice everyone