About priority

[Gokusupersaiya3]

I have 2 questions:

First: If I play Asuza lost but seeking, and my opponent doomblade her, do I have priority to play the extra lands or no? (Since this is an special ability)

Second: if I play a planewalker and as soon it comes into play my opponet destroy it, do I have priority to play its ability?  (Since this have to be played as a sorcery)

[particle]

To answer OP's question, the answer in both instances is yes. You cast your Asuza, she's on the stack. Priority is passed. Your opponent can now respond. If they don't, Asuza resolves. At this point, the stack is empty and YOU have priority again. You'll be allowed to play your lands. Same deal with the second thing. Your PW resolves, and you then regain priority. Once you put the PW's ability on the stack, your opponent will be able to respond to it by killing the walker, but not before you're able to use the ability.

One small note about Azusa since she normally sees play with bounce lands like {Boros garrison} and {golgari rot farm}. Lands like this create a triggered ability that must resolve before any other lands are played. You cannot just slam two {sonic growth chambers} without giving your opponent priority. So Azusa resolves, you play {simic growth chamber} I respond to the bounce ability with {doom blade} before you can play your second land. Doom blade will resolve before you can play the 2nd extra land. Once Azusa dies you no longer get those extra land drops.

[Mr_Fahrenheit]

And with the planeswalker question, that doesnt just apply in the situation described with moving to second main phase. Once your planeswalker resolves you get priority, but if you make any action other than activating one of its abilities your opponent can respond with a heros downfall and you will be unable to respond with using the planeswalker's ability.