MTG Salvation

My question in generalized form to aid in forum searches:

• Two cards trigger at the beginning of a phase, the first card destroys the second card, does the second card's effect still trigger?
• Two cards trigger at the beginning of a phase, do you choose the order the cards trigger?

Cards in question:

• Serenity
• Paradox Haze

My question:

1. I currently have 2 Paradox Hazes in play. I then play Serenity during my turn. During my next turn, am I correct in that Paradox Haze would trigger first because it was played first and then Serenity would destroy Paradox Haze, allowing me to keep the extra upkeep for the turn.
2. (Starting out with nothing in play) If I play first Serenity and then Paradox Haze during my turn will Serenity destroy Paradox Haze, negating Paradox Haze's effect
3. I found the following here that indicates that I get to chose the order that my cards trigger if both have a begin at phase trigger. With that said, I believe I could choose to activate Serenity first to negate the effect of my Paradox Haze. Is this logic valid?

The basic rule of thumb is: first resolve
upkeep abilities controlled by your opponent in any order he or she chooses,
then resolve upkeep abilities controlled by you in any order you choose.

Thank you Ninja Caterpie, your clarification fully answered my question.

I've been reading on these forms about "City of Solitude", on how it opponents can't play abilities in a cost:effect structure.

Cards in question:
Temporal Extortion
City of Solitude
Armageddon Clock

Case 1: With City of Solitude currently in play, Temporal Extortion is played, does "City of Solitude" block opponents from paying half their life as that is a "cost" and the effect is "counter Temporal Extortion". As its an optional cost to the opponent, that the opponent would have to pay during my turn. The other 'point of view' is that this is a global triggered effect like most enchantment triggered effects.

Case 2: With "City of Solitude" and Armageddon Clock both currently in play, my upkeep starts, I add a counter to Armageddon Clock. The opponent can pay the cost "4 colorless" to have effect " remove a counter". Would "City of Solitude" block opponents from paying to remove counters on my upkeep? Like with case 1, this is an optional payment by the opponent as its using "may" wording.

Ruling in question on "City of Solitude": 10/4/2004 City of Solitude does not stop triggered abilities from being put on the stack. They are never "activated".

Both situations have an optional cost and effect structure, making it unclear if paying the cost would count as an ability, and thus be blocked by "City of Solitude". Based on the ruling above, these cases might be considered "triggered abilities" and as a result, "City of Solitude" would not block them.