Thanks for the engaging questions! Reading between the lines, I think there's an important point that hasn't come across. Prodigy isn't SaaS --- it's a library you download and run. You can extend and customise every aspect of it, and there's definitely no lock-in. The model (and annotations) never have to leave your servers.
For the specific questions:
1. The built-in web views all have binary annotation interfaces. This is more of a design choice than a fundamental limitation, and the front-end is extensible --- you can add your own web views if you need to.
The binary interface is sort of a position statement. We think this is The Way, so we want you to try it. We'll have more input components in future, but at the start we want to guide people towards the intended workflow.
2. The beta focuses on NLP support, but there's a front-end for image classification, and a workflow page: https://prodi.gy/docs/workflow-image-classification .
3. You can usually get some accuracy improvement by retraining once all the annotations are available. I've not found a streaming SGD algorithm that works as well as the simple iterate-and-shuffle batch process. Batch training also lets you tune the hyper-paramers. You can read more about this here: https://prodi.gy/docs/workflow-named-entity-recognition#trai...
I would suggest writing a Prodigy recipe to do the batch training. That way you can pass in the dataset ID, instead of exporting the annotations. There's no problem with exporting the annotations and running a script, though. Again --- it's all on your computer. You can run it however you like.