Meaning of となら and とやら in these sentences

I've encountered those two words in a manga I'm currently reading. Here are the sentences :

きさまとならまちがいなく勝てるぞ。

I don't know if となら is a specific particle or if it is と+なら(ば) (and in that case is と related to まちがう　or 勝てる?)

てめえの罠にまんまとかかってやる。完全体とやらになるがいい。

I suspect とやら is related to the やら particle and has a meaning close to など... but I have seen somewhere that it is equivalent to one of the uses of the quotation marks in english. Like : You pissed on the rug again! - No I didn't my love, it was the dog! - Right, "the dog"...

Answer

となら

きさまとならまちがいなく勝てるぞ。

In simple terms, this is と ("with") + なら ("if"). Basically,

If it's with you, then there's no doubt I'm gonna win.

とやら

てめえの罠にまんまとかかってやる。完全体とやらになるがいい。

This one I was less familiar with. From the Daijirin entry for やら:

やら

〔「にやあらむ」の転である「やらん」から。中世後期以降の語〕
一 （ 副助 ）
体言および体言に準ずる語，一部の副詞，助詞などに付く。
...
②
〔「とやら」の形で〕 はっきり言わずに，ぼかして言うときに用いる。 「山田と－いう人」 「どこと－抜けている人」

"Used to make something vaguer, without stating something definitively."

So in your sample sentence,

I'm'a let myself get caught in your trap. Go ahead and become "complete" or whatever you call it.