With respect to extensions service - you do not need to transfer it, it can be installed anywhere in the network, it just need an access to vSphere and to all collectors. If you already removed the old one and installed a new one, you can re-assign collectors by changing LicenseServer parameter in the "HKLM\Software\Veeam\Veeam Virtualization Extensions for VMware" registry key, just change it to the new extensions service host and restart the collector.
You cannot transfer credentials from one extensions server to another, but you can transfer configuration(you'll have to manually re-configure passwords for connections) although this option is not supported and we are not recommending it, use on your own risk(I would recommend to re-create connections manually): you just need to copy vemState.db.xml file in folder "C:\ProgramData\Veeam\Veeam Virtualization Extensions for VMware" from one server to another and restart the extensions service.
Good idea about some webinar/video on things you can do with VEShell, although writing PowerShell cmdlets on the whiteboard could be quite challenging
With respect to collector version - it looks like a bug, most likely our patch setup application is not updating registry entries, we'll take a look, thank you very much for reporting the issue.