By calling forth the power of the fire dragon
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a complete idiot.... it is a stupid combination
well... the only way to get adventure quest coins for free is by watching the advertisements given to you by ballyhoo,very rarely you will get 5 adventure coins. also if your friend is about to upgrade to members and he has you on his reffered friends,you will get 200 adventure coins when he upgrades other than that there is no way to get free adventure coins except from battleon points but i wouldn't call it "free"
The effect of Call of the Haunted that destroys the monster it summons, is not something that 'activates'. Because it does not activate, there is nothing for Stardust Dragon to chain to.
Armed Dragon LV 10 can only be summoned with the effect of Armed Dragon LV 7. Once you get that out and keep it out long enough for its effect to activate, tribute the LV 7 to call out LV10.
As long as the Stardust Dragon was summoned properly (ie, it reached the field correctly initially, rather than someone tried to summon it, and the summon was negated) then yes, you can resummon it with cards like Call of the Haunted. That applies to all Synchro Monsters, unless the monster has a specific restriction on it.