Basically, updatable WebView is the same as updatable desktop browsers for example. No one can guarantee that everything will work as expected on the new versions, but still, a lot of testing is done before the official releases. In AppBuilder hybrid development is the same, with the difference that, testing is being done not only from the WebView team, but from our side as well.
The above said, I will now try to answer your questions:
- "Will it behave normally?
It will behave normally and as expected. However, there is a possibility of issues to occur, as not everything can be tested.
- Shall I need to test my app against each web view versions (once it is published)?
This is up to you. It is the same as, if you need to test your hybrid application on each of the available Android versions.
- Is there any way to restrict/notify the user to use the web view version 37?
There are a lot of ways to do this. For example, you can put this as a requirement in the Play Store, or fire an alert on startup of the application. I am not sure if I clearly understand this question, so please, let me know if I am missing something.
- is there any way to set target web view version in my app?
At this stage, I am not aware of such possibility. However, the Android 5 is still new and the good stuff for it is about to be developed.
I hope this helps.