Is it possible to specify the “Distance to Relay” for a specific relay server?
Are there any settings we can configure or add on the relay?
This is being auto calculated based on the hop count from client to relay, you can check the related Retrieved Property for hop count. However you can sync with your network team before implementing a relay in any location to know the best nearest one.
Below link is known for listing all Client settings, you can find many which is specific to relay & use them depending upon your requirements.
You might also want to take a look into relay best practices-
https://bigfix-wiki.hcltechsw.com/wikis/home?lang=en-us#!/wiki/BigFix%20Wiki/page/Relay%20Health