Is it possible to load music from my I tunes library onto my non-apple smart phone?
Can I copy my purchased music from my library onto my Andriod based smart phone?
If so, how?
That depends on the device but has absolutely nothing to do with iTunes.
Connect the device to the computer.
If the computer detects the device as a removable drive, copy the media files desired to the device.
There is no syncing between iTunes and non-iOS devices.