I need help ripping animations from .apk files (android games)

[gameripper]

I am interested in ripping character animations from several Android role-playing and RPG games

This is too vague, it depends on the game engine used. Several engines can export to an Android APK game, and each has its own directory structure / file formats.

Give a try to GAME RIPPER, it is capable to autodetect and rip from multiple engines (Unity, Godot, RPG Maker, WolfRPG etc.). If you're lucky then ripping is simple as:
1. download and extract GAME RIPPER
2. run it
3. drag'n'drop your .apk file onto its window
4. click on the "Sprites" tab to see what was detected

After researching, I could extract the APK file from the game on Bluestacks and export it to my computer.

Just rename the .apk to .zip, and you'll be able to extract it on your computer (with WinZip, 7Zip etc.). No third party service needed.

I also extracted several files from the original APK file; however, I am lost on what to do next. I do not know where these images/animations would be or how to extract them properly. Hell, I don't even know what most of these files do/mean.

GAME RIPPER converts obscure formats on-the-fly, and it can save sprite sheets in PNG and animated GIF formats. It also shows thumbnails on the "Sprites" tab to make it easier for you to select.

But again, APK is just a container (literally just a ZIP archive), it mostly depends on what kind of game engine was used to create the game. GAME RIPPER can be used to rip from almost every common engines, but not all android games supported.