Remote update - Required user rights, continuos operation, license timeout, support of old version

When connecting on TeamViewer, I get the Notice to update to the latest version (currently in use 11.0.93231 on the Remote Computer and 13.2.26558 on my local one), so I have the following questions regarding the "remote update" and the licensing:

1) Do I need admin rights on the remote computer I want to update?

2) Will it be possible to connect to the remote computer right after the update or do I need to "locally" start TeamViewer on the remote computer after the update?

3) I'm a free user and currently my connection gets terminated (which was not the case when using Team Viewer the last time) and when reconnecting, I get the notification that the session duration is limited due to my license. Will that change back to the normal "free" usability after the update?

4) Until when the latest do I need to update the remote computer?

Thanks for your support!