Not very user friendly but you can do all of the above, and more, with the Android Debug Bridge (adb) command line tool. Note that you need to enable debug connections first.
The tool is part of the Android Developer Studio which is free and cross platform so will work on:
- Microsoft® Windows® 8/7/Vista/2003 (32 or 64-bit)
- Mac® OS X® 10.8.5 or higher, up to 10.9 (Mavericks)
- Linux GNOME or KDE desktop
As a developer tool it can do just about anything, including potentially breaking your device so I would strongly recommend testing what you would like to do with one of the emulation packages before trying with your phone.
The good news is that as it is a command line tool you can write batch scripts to perform actions that you do regularly, e.g. backing up all contacts.
- You can copy any file, or directory hierarchy, from and to the device including pictures, contacts, etc.
- You can list installed software, uninstall it, install from .apk files, install to non-default locations - this will break some apps.
- and of course you can start to develop your own apps.
Some examples, (all assuming that you have exactly one device connected via USB):
Tow install some app:
adb -d install C:\SomeDir\some_app.apk
Or to copy your music that is on your SD card to the local drive:
adb -i pull /storage/extSdCard/Music C:\Music
An introductory video is available here or at tutorial is here.