What does the 3-figure code below the value code mean?
While it is possible they are date codes, there are other things that they could be, and it is not universal as to what manufacturers use the space for. Some other examples of what they can be:


It can be the the temperature coefficient and multiplier along with the tolerance. Several of the examples you give are in a format which matches the description here.
Some place voltage ratings (probably not in your examples)
Another option is capacitor series - basically a marking the manufacturers use to indicate what product family they are part of.