This actually presents a conundrum. If you acquire a system with good selling price but no rings, that system will lose their value since you can no longer use mining to generate merits in the system you just acquired.
That's good, though - mining is already one of the strongest actions if carried out in the right place, so having it not always be available is a more interesting balancing factor than nerfing its per-tonne value so it's more comparable with bounty hunting or powerplay commodities as an "always works".
How often do planetary rings regenerate their resources? I legit don't even want to play the game any more at this point because all the stronhold/fortified systems that have rings in are depleted
Depleted/Minor/Major/Pristine is a permanent property of the system and can only change by direct Frontier intervention, which is rare (I can only think of one time).
However, core mining isn't affected by the resources property - only laser mining is - so you can use that even in systems closer to the centre of the bubble.
Also, if you find an Exploited system with good laser-mining pristine rings, you can boost it up to Fortified by selling locally and then use it to acquire more systems.
I thought with 0 demand you just couldn't sell to that station
There are two types of "zero demand" - and in both cases, you can sell the cargo if you want.
1) The station's economy wants the commodity, but already has had lots of it sold recently. You can still sell more (the demand just goes further into hidden negative numbers), just not for the best price. (Though with the right BGS states, some zero-demand markets might have a better price than the average max-demand one)
2) The station's economy doesn't want the commodity. In this case it'll only show up on the market at all if you happen to be carrying it in your hold, and it will sell for an extremely bad price if you try to dump it anyway.