Well, in the RWBY universe, Jaune Arc has a lot of potential for different character interpretations in fanfics. The idea of him being a monk is really interesting. It could involve a whole new set of skills, a different backstory, and a unique role within the RWBY world in the fanfic. But as for whether such a fanfic actually exists, it would require some searching. Some fanfic authors might be inspired by different cultures' concepts of monks and apply it to Jaune's character, perhaps giving him a more spiritual or disciplined aspect that we don't see in the original series.
There could be. Given the creativity within the RWBY fan community, many unique interpretations of characters are explored in fanfics. Jaune Arc being a monk in a fanfic isn't too far - fetched. However, I'm not sure if there's a well - known or widely - read one specifically. You might have to dig around in the RWBY fanfic sections of various websites.
The best chapter pointer here is Chapter 247, "Madam, Your 2000 Kilograms of Sweet Potatoes, Please Check and Accept". It opens with Facts have proved that arch-enemies often understand each other the best. and closes on Why should he expect food without contributing?] [Support!.
If you want the clearest chapter reference, go to Chapter 229. Early on, Huo Ziyang's face had already turned deathly pale.; later, the chapter leans on Huo Xuan, how did she come to know about this?!.
If you want the clearest chapter reference, go to Chapter 219. Early on, Qi Tianyu was somewhat freaking out.; later, the chapter leans on The eagerly anticipated bed of roses had turned into pink roses..
The best chapter pointer here is Chapter 223, "Pigpen Live Stream". It opens with So, for the first time, Jiang Yan, who had always styled himself as the... and closes on The damned Jiang Li was tricking him again!.
The best chapter pointer here is Chapter 244, "Come, Let Brother Give You a Kiss". It opens with LOL, Director Sun can't seriously think his sappy quotes are working, can... and closes on I don't really have much to say..
Chapter 233 is the strongest chapter-level answer because it starts from [What the hell, what's this about life span ending?? and follows through on After all, a real big shot's birthdate wouldn't be so twisted, could the....
A practical answer is Chapter 269, because it turns the idea into a concrete scene. The chapter opens with The next morning, Shen Lan's personal account posted a Weibo., adds pressure through Too excited to remember to switch to his alternate account, he..., and ends on At that time, people.
Chapter 216 is the strongest chapter-level answer because it starts from The production team also took advantage of the situation to start an... and follows through on However, the next second, He Yun, who had hardly ever spoken to him,....
Chapter 219 is the strongest chapter-level answer because it starts from Qi Tianyu was somewhat freaking out. and follows through on Having any yield at all was already the show giving them face..
The best chapter pointer here is Chapter 226, "Live Fortune Telling!". It opens with What was all that before then? and closes on Are you sure you can be on the list of winners?] Zhou Xu: [?.