You can use your same license key in this case, it's no problem! The licensing agreement for BuildMaster and Otter explicitly permit dedicated dev/test instances.
ProGet requires a separate server... but if it's just a temporary migration then it's also OK too.
This is OS & .NET Framework dependent.
Many users have reported that setting the follow registry will resolved this issue:
Key: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v4.0.30319
Value: SchUseStrongCrypto
Data: 1
Note that this will involve a reboot. See this guide on TLS in .NET for more information