All questions are answered

Contact me if you do not find what you are looking for
No. For now it is a personal timer. But in futur release you'll be able to share your timer.
To install for all of your users, contact your GSuite admin who will be able to install onto all the user accounts in your team globally. Information on how to do this can be found here
No. The plugin doesn't store any personally identifiable data from any of its users.
No. The plugin only add a timer. Their is no informations shared or recorded from your call.
Yes. Forever.