Regarding saving, I think it depends on how you use tflite.
1. If you 're using SELECT_OPS, then you are using FLEX delegate. I assume the tflite team have implemented the save and restore ops
2. If you're using custom ops, then you'll have to implement save and restore custom ops your self. Depending whether you want compatibility with TF or not you can either implement the way save/restore are implemented in TF, obviously using what tflite offers you, or if you don't care for compatibility, then you can devise you're own implementation
Regardless case 1. or 2. when creating you .tflite model file, wou will need to add extra two subgraphs, one for saving and one for restoring. So you're model will have at least 4 subgraph. An inference subgraph, a training subgraph and the extra Save & Restore subgraph. The names are up to you, as long as call the correct signature runner.
Hope haven't forgoten something