The database only holds player personal information, league information (name, notes, who belongs to the league) and season information. All statistical data is saved within each tournament file. When you generate statistics on the Stats tab, the software loads each tournament file and tallies all of the information.
So, you don't *need* two different databases, although that is certainly one route you can take. I, personally, would opt for not having two databases. If you want to use more than one database, you'll need to become familiar with the Data Store feature. You can create, initialize, delete, and select Data Stores on the Preferences tab (press the Data Stores button). The Data Store holds the database, and is the default location to save templates, tournaments, exported files, etc. So by having more than on Data Store, you can have multiple, independent databases.
In my opinion the better route would simply to utilize leagues and seasons to partition the players in your database. When you want to generate statistics, you create filters that select the appropriate league, and you'll get statistics pertinent to the selected league.
Is it also possible to click on a particular player and see exactly how many points they have for both leagues.
No, this is not possible. You'll have to generate stats for the two leagues separately, as I noted above, and there's no way to have a combined view of them.
Once you've run stats, you can print the table by pressing the
Export button on the Stats tab; there will be a Print option on the dialog that opens. Not exactly intuitive, I know; maybe I need to add a
Print button.