Destroying Set Down Spell/Trap Cards

Because they used the 2 nd chain ,which actiave before chain 1 .

They can activate that target before the card that will destroy them resolves

Oops, I just read the title lol.

When you destroy a SET spell/trap card, they can CHAIN that set spell/trap to the card you used, and activate their effect.

Now the next scenario is more tricky :
#1 Some cards say ''Target a set card and destroy that TARGET'' and #2 some say ''Target a set card and destroy IT''.

TARGET =/= IT. In #1, if you target a set spell and they activate it to make it face-up (for example, you use 'Nobleman of Extermination' on a set 'Mirror Wall'), the set card won't be destroyed, because it will no longer be a SET TARGET anymore (it's now a face-up target). In #2, the set card will be destroyed no matter what.

I invite you to join the Duel Links reddit if you have anymore questions.

Because the activation resolved, so the effect still goes off.

The card you use only says ''Destroy it/that card/that target''. (see Twister for example)

It doesn't say ''Negate the activation, and destroy it'' (see Ultimate Providence for example)

You must be a newbie to this game. Welcome!
You need to distinguish 2 terms of word, NEGATE and DESTROY.
If you just DESTROY a set spell/trap card(s), your opponent still could activate them in responding to the destruction. You must use a card that says NEGATE to prevent your opponent from activating those effects.
Btw, there are some destroying/negating cards which specify that cards and effects can't be activated in responding (for example: Night Beam...).