None of those abilities break stuns, but stuns do not stop them once they start. It sounds like you just have bad internet speed or high ping, and are seeing the ability animations after they are actually used.
The general rule with hard CC and dashes is that the CC is applied at the end of the dash, without stopping any damage the dash would do (which is weird in some cases, but makes sense in others). Some forms of displacement stop certain dashes but not others; for a while, charm made the target immune to rocket grab and a few other pull/push abilities.