All app icons not showing up in my home screen
the apps on the homescreens in Android are to all intents and purposes shortcuts, and not the apps themselves. 

You should but don't have an icon in your dock (the lowermost part of the homescreen) that opens this app drawer.

The icon usually looks a bit like this: 

http://cs3-1.4pda.to/4714358.png

This image shows: Google Now, then your homescreen, note the middle icon on the bottom, and then the App Drawer opened (very right of image). This is the list of all your applications. 

You could try (I don't have a similar device) long pressing on a free part of a homescreen and see if you can add an action, or shortcut to the app drawer. 

Alternatively a launcher like Nova Launcher or indeed Google's own "Google Now Launcher" are free and have this option. 

Here is an example of adding an action in Nova Launcher which might help point you in the right direction (note app drawer):