The dome will be an open skeletal structure. Probably with anchor points to hoist up a cover of sorts in the rain. Never thought of the acoustics inside a closed geodesic dome. I can easily see how it could be a nightmare! Frankly, I think geodesic dome houses are ugly. Here's a concept sketch. Dome might look like this. Or might not.
Not gonna lie. I LOVE that dome. A suggestion? Rather than have this big beautiful open thing that's going to require you to hang tarps in the weather, you could perhaps build it as the cupola of a gazebo... you'd have to sink footings, yeah, and you'd need some columns... but columns are just an excuse to decorate, as you've proven. And then you could shell 120 degrees or so of it (temporarily or permanently - dunno how much you care about wind loading where you're at) and have a legit performance space. A shell, a half dome and an acoustic guitar is a recital. No amplification needed. My mother used to hit 300-person weddings with a shell and a string quartet.