destruction + negation

this is a common mistake made when people read card effects,

when a card is activated with the effect to negate another card is played, this means that the other cards effect will not be applied, this also counts for a summon for example

when you synchro summon blackrose dragon http://yugioh.wikia.com/wiki/Black_Rose_Dragon
and the trap card solemn judgement http://yugioh.wikia.com/wiki/Solemn_Judgment black rose dragons effect to boom the field will not happen as it has effectivly not been summoned.

this is different to the destroy a card, cards such a dust tornado http://yugioh.wikia.com/wiki/Dust_Tornado beacuse they do not have the effect to negatem so the effect will still occur, for example.

heavy storm http://yugioh.wikia.com/wiki/Heavy_Storm is played and someone activated dust tornado, tornado will still destroy the heavy storm, but the effect to destroy all spell and traps with occur.

Exactly!
I'm So Tired Of People At My Local Library.
Trying To Cheat Saying Heavy Storm and such doesn't Work

My question is to know when how priority comes into effect when monsters first hit the field. Do all trigger effects get it or just specific ones. And also, when a trigger effect has been activated but the monster leaves the field, sometimes it resolves and sometimes it doesn't according to rulings. How do those work? Finally, can you call priority with spells and stuff?