You need to copy olddb.sql file to your new host. You may use FTP programme to download the SQL file from old host and then upload to the new host.
Sphinxsearch is believed to be the fastest search engine. It is very much useful for large websites. Sphinxsearch can only be installed in a Nginx server.
Your PHP installation appears to be missing the MySQL extension which is required by WordPress. Run: apt-get install php5-mysql in hosting account.
After changing hostname of your VPS, you need to restart VPS (Type sudo reboot in command line). This will solve the issue, “Unable to resolve hostname”.
Linode 1 GB is a good start to host single or multiple websites. It costs 10 USD per month. We recommend you buy VPS hosting from Linode only because it is awesome.