Fan not hooked up correctly making coolant leak?

[Mimm]

Good evening!
I have a 2010 Toyota Yaris that seems to have a leaking coolant issue. I backed my car up, ready to leave when I saw I had a puddle of something under my car. After checking it was clear it was coolant. When I looked under the hood my coolant level was at full, but I did notice something else a little odd that might have caused the leak. I don't fully understand what everything is under the hood, so I have a picture:


You see the little, black clip that is on the upper right side of the picture? Both of those are not clipped on, and after I drove it back into the parking space I noticed you could hear it rattling a little.

Side note: I just had my car in for a recall and also oil change with tire rotation. I'm very sorry if I am not giving enough detail, I don't know much about cars >_<

Another, blurry picture:


Any help would be amazing, I do have an appointment to get it looked at but I am a little worried so I thought I would check with all you smart kids.
Thank you.