I have these messages in Pi-hole diagnosis.
I don't understand the first one. It keeps appearing when I first start Pi-hole.
I also don't know why I'm getting the second and third ones. These clients aren't doing anything abnormal.
Any help? I keep getting these warnings from time to time.
I can't speak to the 1st error but rate limiting is caused by client behavior. Have you looked at the dashboard / query logs for the timeframe in question? Depending on your traffic volume, they ususally standout as large spikes.
LOL - I would say that qualifies as a spike 
In this case, I should investigate what this device was doing, right?
Yes, if you look at the client activitiy windows on the dash board ( bottom graph ), each client is broken down by a color. In this case you can click on the light blue section of the graph and it will pull up what that client is and what it was looking at.
You can sort it and get and idea of what domains it s accessing by flipping through the pages.
You can also do a sqlite3 data base query that can help. I'm not well versed in that though. Perhaps a Dev / Community Member could help with that. The basic search I've outlined above is often enought to point you in the right direction.
Actually, the blue one is pi-hole itself.