For the "host" field in your settings file you'll need to put the IP of the server followed by a colon followed by a port. If no port is given, 3306 is assumed. Make sure you have the right IP address and the right port. If it still won't work, contact your old host.
Uhm... no. That's not load balancing. Where in the world did you hear this?
You can't point a single domain to multiple nameservers. If you do, the first two records will take priority.