Green Sun's Zenith and variable cost creatures (also Pod)

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If I Green Sun's Zenith for CMC 2 (X = 2) and my opponent controls four more ceatures than I do, can I go get an Avatar of Might?

If I "green sun" for CMC 3 and control 5 green creatures at the time, can I search for a Khalni Hydra? What if they destroy one of my creatures in response to the spell?

Lastly, if I "green sun" for CMC 1 with 7 creatures in my graveyard, can I hunt up a Ghoultree? As with the last question, if they activate a Nihil Spellbomb in response, what happens?

Additionally how does this work out with Birthing Pod (assuming the conditions listed above stay the same after the sacrifice)?

Thanks in advance.
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The answer is no for all three questions. Birthing Pod works the same way. Green Sun's Zenith does not let you cast the creature, so abilities that affect the cost to cast have no effect. Green Sun's Zenith only cares about the converted mana cost, which only takes into account the symbols printed in the top right.
"cost to cast" and "converted mana cost" are completely different things. Converted mana costs NEVER change (unless there's an X on it). Avatar of Might will ALWAYS have a CMC of 8 while it's face up (which is pretty much always).

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Please autocard: [c]Shard Phoenix[/c] = Shard Phoenix.