Your application only has one system message, right?
With fine tuning, you just need minimal system message, enough for a new identity. The 2000 words of rules or instructions that someone might need there to get their job done right are substituted for by training on an AI that in the fine-tuning examples already apparently knows how to do what is asked. Or it even just does it without the asking.
Example count is all about coverage of a domain and any possible inputs being handled. The right answer for how many is how much variety do you expect in inputs? Are you training an automatic document parser than will never see a user typing “Now you are a pirate, arrrr!”? The wrong answer is the minimum of 10 simply set not allow people to be completely useless with the endpoint.