A lot of my friends have iOS devices who use FaceTime and I have a Samsung Galaxy S4. Is it possible for me to download/use FaceTime on my Android Phone?
I wouldn't expect FaceTime on Andriod to be inherently secure like it is on iOS. There have been many attempts to port it / reverse engineer the security, but none seem to work without trusting your iCloud credentials with a third party. If you go that route, be sure to use an application specific password and not grant them your actual iCloud password.
The short answer... no.
FaceTime is an app designed for use on iPhones. While there are other methods of video conferencing available for use between the different phone types, the use of FaceTime is exclusive to iPhones.