Thanks a lot for playing and for the detailed notes! Glad the first-night Strength upgrade clicked.
To answer your question: orders are optional bonus money, there's no penalty if one runs out. You don't need to focus on them either. Count orders like the 6 × Milky quartz fill up on their own as you break geodes in that zone, and you still sell the gems as usual. The one thing to watch: they only count in the zone where the client asked, so if you move to a new zone before finishing, that order stops progressing.
In short: mine as usual, save for rent, and the order is a nice extra when it completes.
You're right that the card didn't make that clear, though, so I've just added a small "BONUS" stamp to the order notes (update 0.7.9) so nobody wonders whether it competes with the rent. Thanks for pointing it out!
If you get to the coin flip at some point, I'd love to hear whether it felt tense in a fun way or just unfair.