Dark world

Q1) I activitate card destruction, I discard grapha,broww,snow in this order. So I after I discard, I search via snow effect, draw 1, destory 1, then card destruction drawing effect comes in?
Q2) I activate drag down 2 grave, I only have MST on hand, oppenent choose 2 drop MST, can i chain MST and still draw 1 card?
Q3) I have 1 gate of DW on field, I activated it's effect, then i replace it with another gate, am i allow to use the gate effect again this way?

1) Card Destruction's drawing effect will come in first, then you may choose the order you want to activate the effects of your Dark Worlds.

2) Not too sure.

3) You may activate the effect of the second Gate.

for 2 dont think so if not mind crush would be useless against quick play spell cards

You can chain before Dragged Down To The Grave resolves, and make MST chain 2, but after MST resolves, Dragged Down cannot be resolved since you do not have a hand card so it CANNOT resolve.