Mouse on iPad running 13.4

There is no generic support for battery-level display. Generic mouse support is limited to basic mouse functions. Full support, including battery-level, is included for Apple Magic Mouse 2 and Magic Trackpad 2 only

No.

You are free and welcome to submit feedback about this issue to Apple.

This is only one of the few ways to directly contact Apple about ANY product issues.

iPad Feedback

http://www.apple.com/feedback/ipad.html

Cognizant Apple employees read ALL feedback generated from all of the various feedback pages and transfers the data to the proper and responsible Apple teams and personnel, but NO Apple employees will ever respond with any type of direct, individual replies from the feedback you post.

The more users that post product feedback about any product issue, the faster Apple, in California, is made aware and starts working on a fix/solution for a future software update.