You would need to query the members of the group using Get-AzureADGroupMember and run a ForEach loop to add the members to the new group (using Add-AzureADGroupMember).
Example script:
(Get-AzureADGroupMember -ObjectId xxxx -All $true) | ForEach-Object {Add-AzureADGroupMember -ObjectId xxxx -RefObjectId $_.ObjectID}
Satheshwaran Manoharan has provided a great step-by-step blog post here that achieves this and walks through each step.
To update the OtherMails property you would need to use Set-AzureAdUser and most likely import all of the user info into a CSV as described here.
Let me know if this helps and if you have further questions!
Additional example from Stack Overflow:
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