We would like to have subfolders within a project folder - even just one level. We often have large/long projects where each version/iteration has separate and distinct mockups, and would be easier to organize this way.
That would be possible in Balsamiq cloud
you can read about the feature in full here: https://docs.balsamiq.com/desktop/overview/#using-mockup-hierarchy
Yes and no
In myBalsamiq we do not have the feature and I am so bold and say it will not get it.
We rewrote our web application and it caught up with the features we developed in our other products.
In Balsamiq Cloud you can use the hierarchy feature Heringsfilet mentioned.
You can export your myBalsamiq project to a bmpr project and import it in Balsamiq Cloud.
You find details how to do that here.