do you get a notification if someone toxic was muted?

When they initially rolled out the Instant Feedback System, it leaned more towards catching behavioral infractions. One of the main reasons for that, I suspect, is because of how much easier those sort of things are to prove. If someone is using racial slurs in chat, it's there in writing as irrefutable evidence.

But it's a bit more difficult with the trolls and int'ers. Sadly, they are not all stupid enough to build 6 Tears of the Goddess' on Riven and go 0/25/0 in lane. As far as the intentional feeders, what's the main difference in a guy who goes 0/9/6 as adc because he's intentionally feeding after his support took one cs and a guy who goes 0/9/6 as adc because he's a Bronze IV mid main, and triple-queued with two friends who have almost double his normal mmr and he ends up against a Diamond V Draven main? To the other teammates who aren't queued with him? Probably very little difference. He still looks like a feeder, and it can still get him reported by that fifth player on the team. To the system? This is the big question. It has to break down things like items, cs, when and where deaths occur. So many different variables, and Riot does try to err on the side of caution, and not punish players for just having a bad game, or even a bunch of bad games. Players are allowed to make bad decisions. It just gets them put in lower ranks.

I believe the IFS does actually punish for the other categories (trolls/int'ers), but I'm not 100% positive. The top report category covers griefing, which from early support articles included things like throwing the game, or specifically trying to give the enemy team an advantage (inting should fall under this one too, I guess?). Perhaps if one of the Arbiters pokes in here they can confirm whether the IFS covers them.

As far as those pop-up alerts, the IFS had been active for at least 2.5 years before I ever saw one of them. Granted, I don't see many situations where I have to report players, but I have submitted reports, and like you and other players, I had begun to wonder if my reports just never mattered because I never saw any evidence. And all of a sudden, in the last 6 months, I've seen 3 of them. I couldn't tell you which players it was I reported, or what I reported them for, and I didn't actually stop to read the pop-ups closely to see if they said the same thing each time. (I fail!) It's entirely possible that everyone sees the same pop-up no matter what they reported someone for.