Sylph Wizard alternate FC bonus question.

[villadelfia]

A Sylph Wizard can choose to take an additional +1/2 each level to the effective level for a school ability she possesses. (With a maximum of +4)

My question is, does this only apply to the part that says things like "You receive a bonus on initiative equal to 1/2 your wizard level", or does it also count for the part that follows "At 20th level, assume that you always roll a natural 20 for initiative"? If I were 16th level with the bonus taken 8 times (making it effectively level 20), it would give me +10 on initiative, but would it also add the natural 20 part?

I need to know for this concrete example: I have a 7th level Air Elementalist Sylph Wizard, with the bonus taken 6 times in Air Supremacy (giving me an effective level of 10), do I get the Fly at will that Air Supremacy grants at level 10?

[Starglim]

Only to the effect of abilities you already possess that vary by your wizard level. In the example, you'd get a +5 bonus to initiative.

[villadelfia]

Starglim wrote:

Only to the effect of abilities you already possess that vary by your wizard level. In the example, you'd get a +5 bonus to initiative.

And in the example below that? Note that Air Supremacy says that it gives you fly at will at 10th level.

[Medusil]

1) Choose one school ability
2) Calculate your level with the bonus
3) Determine all effects (plural!) from that ability as if you had that level

So yes, if your level with the bonus is 10, that ability and all its effects would function as if you were level 10.

For example: If that ability would allow you to lay eggs at 3rd level, speak in palindromes at 9th level and interpret RAW at 15th, an effective level (with the bonus) of 10 would only allow you to lay eggs and speak in palindromes. You would still not be able to interpret RAW.

In the above example for the sylph favored class option:
"Select one arcane school power from the air or wood elemental schools that the wizard can currently use."

So yes, you need to have access to the ability before you can choose to take your favored class option for it.