Close! 1) Since she's left her desk on a whim, you can put your present on it. 2) Since my dog is vagarious, I have to keep my eyes on him. (This is still very strange. We don't use "vagary" in common speech, but I've corrected the noun to make the adjective you need: vagarious.) 3) She has been subjected to the caprices of her little child. (You can use "subject" as well.)

These sentences are great explorations of the meanings, but I don't think they are very natural!! Here are a few! 1) She leaves her desk frequently "on a whim" and the teacher is getting frustrated because she doesn't ever ask for permission. 1A) I picked up learning English on a whim 10 years ago and now I'm fluent!! 2) He acts upon every vagary, every caprice, every whimsical idea that floats through his mind. He never really sticks to his resolutions. 3) He has no sense of respect for other people's time. Every whim, every caprice, every vagary his mind comes up with, commands his attention. He never settles on anything!

I understand. I will use "whim" in daily conversation. Thank you very much.

I forgot to mention, 3) She has been subjected to the caprice of her child. And to be honest whim is the only word I might hear in daily conversation. I'm not sure about in other places!! These terms are more literary!