For your first problem, prioritize keeping Huton up but don't waste a Ninjutsu refreshing it if you have plentry of time left on your buff. Use Trick Attack whenever it is off cooldown. Keep Dancing Edge up constantly unless you have a WAR tank providing the slash debuff consistently for you so you can focus on Aeolian Edge instead. Lastly, keep up Shadow Edge and Mutilate when you are able. With pracitce, you should be able to keep everything active nearly 100% of the time.

While Huton is active, use Raiton if you have good latency and especially if Foe Requiem is being used. If latency is causing issues, use Fuma Shuriken as it will be buffed by Dancing Edge and only needs a single mudra.

For your second problem, it is a known issue. It isn't a bug, it's just lag which is really pesky for some and not so bad for others. For me, I don't have issues most of the time and can fire off mudra no problem. For others Ninja is relatively unplayable because mudra are unreliable with the lag. Hopefully it will be addressed sometime soon-ish.