The answer to both questions is : "depends on the pool".
Since you're asking in the Apache/Tomcat forum, I'll talk about Jakarta's Database Connection Pool (DBCP).
1) the pool instantiates connections 'as needed' up to the configured maximum number of connections.
2) you can configure DBCP to do a verification query (for example, "SELECT 1").
All the settings for DBCP are documented here:
http://jakarta.apache.org/commons/dbcp/configuration.html