What would be the best way to do a 2D Avatar Creator without using an game engine (ie. Unity)?
The avatar images will be a basic body and placing different images for the different body parts - head, body, legs, arms, etc. Layer the different images on top of the base image.
Can this be achieved in a regular Android app without using any sort of a game engine? Are there any libraries like this already done?
For a 2D Avatar Creator, using a game engine for a job like that seems overkill (a library might be too much as well).
Coding it from scratch is much simpler than having to deal with a bunch of unnecessary tools that at the end of the day just take space. Also, it is much more efficient, as you only code the bits you need.
Because you want to make this app for android, I'd recommed doing so using the official Android SDK. It includes Eclipse (a very nice IDE as well as the most popular) so no need to worry on what else to download.
This SDK requires you to use Java (If you haven't learned this language yet then do so. It's probably the best and only language you'll need to know).