Refer following MS article and configure pass-through authentication so that replication can be set up between domain and workgroup

http://support.microsoft.com/en-us/kb/321822

HTH

Usually you will find it at the same place where copy of .trn files have been kept on secondary server.

HTH

There are many factors affecting the database maintenance plan based on the application and type of database and environment. However primarily you can focus on backup strategy, High availability, Database...

Just curious: Are you able to take the backup from Query Analyzer executing command like:

BACKUP DATABASE <dbname> TO DISK = <specify_path>

If getting any error please post it here.

HTH

I guess firwall/port might be the issue. Can you try to telnet the port you are using for sql server which is accessible after VPN?

HTH

You can also check the I/O performance of storage before you hand it over for production. Also try all the possibilities of fail over to check the cluster e.g. reboot...

I guess there is no SQL Server issue. Are you able to run SQL SERVER in the physical network which are you connecting through VPN? Connecting/disconnecting the VPN might have...

While executing your transaction you can use hint "TABLOCKX" refer following MS link for further details.

https://technet.microsoft.com/en-us/library/aa213026(v=sql.80).aspx

HTH

check if you can use Try...Catch in your SP for error handling.

HTH

http://www.microsoft.com/en-in/download/details.aspx?id=29066

HTH

+1

If possible, plan distributor on the separate machine to reduce load on production box.

Are you missing any settings/fine tuning on .net?

.Net application connects remotely? or from the same server?

check your error log are you getting error 3409? If so visit following MS link:

https://msdn.microsoft.com/en-us/library/ms187743.aspx

HTH

To gauge memory and CPU create a dummy load expected on the application database and stimulate the environment as production. However calculate the expected future growth and keep the buffer....