Add downloaded components to existing library in Altium?
Open the various individual libraries in Altium.
Open the your new target library.
Right-click on the component, in the component panel list, that you want to include in your new library, and select 'Copy'.
Right-click in your new library and select 'Paste' in the component list.

This works for both Schematic and PCB libraries.
Going from Eagle to fAultium is a big jump.  Read the docs.  Join the Official Altium forum ( https://forum.live.altium.com ).