How do I deploy an SSIS package?
How can I tell which type of deployment a package has taken?

Look at the definition of your SQL Agent Job Step. 

If it specifies /file then the package has been to deployed to the file system somewhere.

If it specifies /DTS then it's using a well known location on the SQL Server installation path (precise location eludes my memory as of this posting but \Program Files\Microsoft SQL Server\XXX\DTS\Packages and/or C:\Program Files (x86)\Microsoft SQL Server\XXX\DTS\Packages are good guesses)

If it specifies /sql then it is deployed to the specified SQL Server in msdb.dbo.sysdtspacakges90 (SQL Server 2005) or msdb.dbo.sysssispackages (SQL Server 2008/2008R2+)

As to scheduling a package that you can't see, this sounds suspiciously like you're not on 2008 R2 as you think but much more like 2012+ as this is the SSISDB with the folder/project/package structure. If this is the case, packages can be specified as being Entry Point Packages or not. It's just a UI convention, there's nothing that prevents them from running. There's a selector that specifies whether you want Entry Point Packages or All. Switch to All packages