Can applications be downloaded without a Google Account and without disabling security features? If I wish to install applications such as Skype, DropBox, etc however without registering for a Google account, is that possible? If so, how do I install them without a Google account?
Use ADB to install the applications.

Install the Android sdk ( https://developer.android.com/sdk/index.html ).

Enable USB debugging in Settings>Applications>Development.
This process can be done even without enabling side-loading of apps. Open a command prompt window and type:

adb install app_name.apk