When I last made an installer for a VB6 application I used the nullsoft installation creator, which is very flexible and useful. I believe you can include a DLL with methods to be executed as part of the installation process, which could then be used to verify license keys and store some authentication data in the registry or elsewhere.
As for database access, yes you can do that still, you need to reference ADODB, which you may need to install if it is not present, and you can connect to all sorts of databases. At work I still support some old VB6 code which uses Sql Server for both SQL queries and stored procedure calls.