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Is the Yncarne allowed to arrive on the battlefield when a unit is destroyed turn 1? Also, is she able to arrive via normal deepstrike? (away from enemies more than 9")

Yes, the Yncarne can arrive turn 1, but not in Eternal War missions (Matched play) as they have no exemption to this restriction.

The Yncarne can only use it's rule to arrive, which only happens when a unit is destroyed, it can't choose to arrive at any other time.

so in the chapter approved GT packet, she's able to arrive turn 1 via the death of a unit?

No unit can come in turn one in the Match play rules (aka GT Missions) unless it has a rule that says otherwise (see drop pods). When the Yncarne starts on the table it has a different rule for teleporting to a dead unit, this can be used turn 1 as it is not arriving from Reserves, look at Da Jump, Black Cornucpians, etc.. for examples.

You're forbidden from arriving from any kind of reserves or reinforcements in turn 1, in both the GT pack and the Eternal War missions - basically, every kind of "Matched Play" mission available right now, so we can reasonably expect this to be the case for other Matched Play missions going forward.
Drop Pods are allowed (...admittedly with some disagreement, but that's a subject for another thread...) because their rule specifically states that they can arrive in your first Movement phase, regardless of mission rules. The Yncarne has no such wording.

thanks guys! Might be better to just start the yncarne on the board

Tricktock wrote:
thanks guys! Might be better to just start the yncarne on the board

Yes you always do, there is no reason not to with Obscuring and LoS.