My terrariums have only mini orchids and jewel orchids- but I think a mini begonia might get along just fine with them! Just gotta find the right variety- but I think you’re right and the moist spag might be my in to the begonia club!

Too much water, not enough airflow! The water has become stagnant, and therefore stinky and gross. Dump all of it out and clean with diluted hydrogen peroxide to remove mold. In a greenhouse and the wild they love water in the cup- in a house you’ll need a fan pointed at it. Or just lightly mist!

Would need a closer picture to be sure but looks like scale. Up close, do those little brown spots look like barnacles? If so- Cpt. Jack’s dead bug brew and some elbow grease. You’ll have to remove each and every one and spray to prevent them from reaching adulthood when they stick. Best of luck!