Hi there!
I suspect there are two issues here. While it’s hard to troubleshoot something that only happens sometimes, the popup sounds to me like a scripting conflict– can I ask you to temporarily disable all plugins except this one and WooCommerce, and see if that resolves the issue? If it does, then you can slowly re-enable the plugins until you find the one causing the conflict.
If the step above does not resolve the issue, the next step is to switch back temporarily to a default WordPress theme like Twenty Sixteen and check again to see if that fixes the problem.
The absence of shipping methods sounds like its own issue– I would check your Shipping Zones and methods carefully, as well as the list of countries you’ve configured your store to sell to. What addresses are you using that give you “no shipping methods available?”
