DNS – Non FQDN fails to resolve on Mobile Devices

NetBIOS is a different thing to DNS. NetBIOS name resolution uses either broadcasts (limited to a single subnet on an ip network typically), WINS (wider scope, requires a WINS server to be identified generally provided via DHCP), or an LMHOSTS file. If NetBIOS name resolution is failing across a VPN connection but working within your LAN environment and that LAN uses WINS then you should look at the DHCP scope options being provided by your VPN client (these may be configured at the client end or provided dynamically by the VPN gateway).

If you mean the hostname (e.g. the MyPC part of MyPC.somedomain.com) does not resolve across your VPN even though it does when you are in your office then the issue is that your VPN is either not appending the domain suffix that you need or possibly that your VPN is not redirecting DNS.

Without a bit more information it's hard to be more specific - post the output of ipconfig /all when connected via VPN and when connected to the LAN for a start.

AD-integrated DNS zones (the kind that replicate via AD) can only exist on domain controllers, as their data source is a directory partition that's read from the local system - directory services replication can't happen to a system that doesn't have directory services available.

A non-DC DNS server's zones are stored locally on the individual system - you can use zone transfers (secondary zones) to get copies of zones on another system, but you can't make changes on that system - this might not be the kind of behavior you're interested in.