Does an alternative host in a Zoom webinar need a Webinar license?

Regarding your primary question if the Alternative Host needs a Webinar License. The short answer is "NO". Here is how it is officially described...

• For webinar, the user who schedules the meeting needs both a license and the webinar add-on; the alternative host only needs to be Licensed

The above explanation comes from this article and also includes potential caveats.

Support Article

Alternative host limitations

• The alternative host can start the meeting using the join link in the email or calendar invite sent to them by the host. The meeting will not display in the upcoming meetings list in the desktop client, mobile app, or web page for alternative hosts.
• Alternative hosts can't schedule on behalf of the host. If you need to schedule a meeting on behalf of another user, use scheduling privilege. You can also give another Licensed user scheduling privilege, which allows them to schedule meetings for you and makes them an alternative host for those meetings. 
• If the original host joins after the alternative host, the original host is given the option to reclaim host-control of the meeting, or have the host-controls remain with the alternative host. If the original host retakes host control, the alternative-host is demoted to a participant.
• If a host is attending a meeting but needs assistance with managing the meeting, they can assign a co-host during the meeting instead of an alternative host. Learn more about roles in a meeting.
• Recurring meetings with scheduled occurrences cannot have their alternative hosts edited for a single occurrence. To modify the alternative host, they will need to edit all occurrences in the web portal.

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