@ivofx Mid/Side vs Stereo is definitely hard to wrap your mind around - much easier to grasp if you come to it from using the microphone technique associated with it than as a mix process, IMHO.
As for floating point to integer: a floating point number has an integer bit and a fractional bit - to convert to integer, you need to round (up or down) or truncate the fractional bit. Which approach is appropriate will depend on the application and there is typically a default approach defined by the language you use if you just convert the types without explicitly rounding (etc.) from floating point to integer - usually this is truncation.
To go the other way, you usually just re-format the integer and give it a fractional bit that is set to zero (this happens auto-magically in the conversion in all computer languages I am aware of.)
If you are truncating an audio signal (say to change it's bit depth, but not as a bit-crusher type effect), you may also hear about "dither", which is a way of avoiding some of the limitations of truncation by adding very low level noise. This is a much more complicated topic, but happily can mostly be ignored unless you need audiophile quality operations.
Hope this helps,