Based on some of my old recordings...you receive a chunk of miranium every 30 minutes, and a chunk of money every 15 minutes(so twice per each miranium receiving). You receive the numbers listed on your FrontierNav screen on the gamepad, which are determined by the probes you have placed on all of your activated FN Spots. edit: The timer doesn't tick while you're in menus, I think. Not sure if the shallow menu that still lets you run around counts or not.
I believe rare resources(or whatever they're called) work similarly, except you receive them every [howevermanyminutes] after setting a mining probe on a spot that has them, so if you set stuff at different times you'll be getting notifications for them at different times than everything else. Or maybe the probe level affects their frequency. I can try and look into the exact times for that today.
I actually wrote a small program that lets you play around with a simulated network of the probes, but I don't think I'll have it 'ready' for other people to use until later in the weekend.
Haha, you've probably answered all of my questions so far. Great information, thank you! Sounds like idling for money is a possibility if one wishes to do so.
e: lmao JUST got the Miranium and money as I was typing this