A: SECast, a lossless converter to cast: SECast. If your tool supports exporting to cast directly, that is always better.
A: In later versions of maya, they added import options. To configure them go to File -> Import (Click the Square) then set your playback settings to match: 
A: Some games may bake their rest positions away, so that while idle, the model will look odd. Importing an animation from the game will make it look normal. You can also move the respected IK Handles if you are animating manually.
Q: When importing worlds into Blender, I get the error "Unable to import instances without a root directory!"
A: You must set the directory where the world models have been exported to in the cast menu tab on the right hand side of the ui: 
NOTICE: The latest cast specification allows skipping this step, if your plugins are up-to-date and tools support the scene directory metadata. If all of those conditions are met, you may have moved the files from their original folders.
A: You can configure your scene to use "Real-time" playback speed, which will match the fps of the animation by right-clicking the timeline selecting Playback Speed -> Real-time this setting will persist scenes: 