Simply use the license manager to "park" your license from your old server. Install version 10 on your new server and activate the liscence. then run the configuration wizard pointing to your database housing the 9.5.1 DB and the configuration wizard will then upgrade the DB to version 10.
You may have to ensure the nodes are all assigned to the propper engine id afterwards.
To resolve this issue perform the following:
Go to Start>Programs>Solarwinds Orion>Monitor Polling Engines
Click on Servers> Poller Load Balancing
Then Select all nodes
Click Polling Engines> Move Selected Nodes to (and choose your new poller)
Then click on Polling Engines> Delete Unused Polling Engines...
Let me know if this resolves your issues.
You can do that. Only thing I will call out to consider is any custom reports you create etc. that reside on the server file system will need to be copied over to the secondary.