How do you start the Ardor funding account monitor via the command line?
There is no specific command line option to start the funding monitor. 
You can probably start it using a curl command after starting your node.

Q: When starting the monitor via the GUI, do you have to leave the browser open?
A: You can close your browser just keep your node running like with forging and bundling.

Q: Also how does fee-ratio work? Is there an example?
A: Fee ratio works like in any other API it is the conversion rate between child token and parent token used when the monitor submits its funding transactions.