1.What are your thoughts on Zuko not being Ozai's son?
I found The Search to be a load of crap when the whole thing with Zuko not being Ozai's son happened. First off, Zuko looks absolutely nothing like Ikem. Bryan and Mike had stated in an interview [pending on source] that Ozai was an older version of Zuko without the scar. Second, it ruins majority if not all of Zuko's character development and reasoning in Book 3.

Uncle Iroh stated in The Avatar and Fire Lord that, "Understanding the struggle between your two great-grandfathers, can help you better understand the battle within yourself. Evil and good are always at war inside you, Zuko. It is your nature, your legacy."

If Zuko is not Ozai's son, then he doesn't have the Fire Lords in him. And makes this whole character development pointless. It in turns only effects Azula who is the descendent of both Fire Lord and Avatar if this is the case. No lie, Azula is my favorite character and I love her to death, but Zuko needs to be Fire Lord for the reasons and was built during the series.

I'm fine with the idea of Ursa having a first love before Ozai and the fact their marriage was forced/arranged on her, but come on! The timing for Zuko to be conceived and be Ikem's and not Ozai's would mean they did you know what at the theater or sometime before that scene. It's the only way to fit with the timing with Ursa and Ozai's wedding which happened right away and they would have consummated the marriage for sure based on the world they're living in. It's poor storytelling with the pacing of the comic and all the stuff that we've been told in the past during the series.

2. What do you think the significant is about the wolf spirit?
Basing off of the symbolism of wolves, is that they are meant for being a disguise. Little Red Riding Hood for example. Granted wolves also have the symbolism of being sexual, "wolf whistle", it's also used for disguise. Then there is Anubis* the Egyptian God. Where it is associated with death and even judgement on the weight of your heart.

So with the wolf my view on it's significance is that it could be symbolsim a disguise to someone either Ikem or Ursa. It could even been a low undertone of the sexual nature since Zuko's blood father is called into question. And then maybe Ursa is actually dead, but I doubt that since the pilot of Korra made it sound like Ursa was still alive when they found her. However, it could have some small connection to the weighing fo the heart in a metaphorical sense.

*While Anubis is a jackal, jackals are sometimes used interchangeably with wolves. And in recent studies jackals are genetically a form of a grey wolf and had recently been renamed to 'Egyptian Wolf'.

3. When do you think we'll officially see Ursa again? Part 2 or 3?
Either at the end of Part 2 or early Part 3. I'm leaning more towards the end of Part 2 to leave all us hanging again until Part 3.

4. What are your predictions to what will happen to Azula after 'The Search'?
I hope for the best for Azula that she becomes one of Zuko's advisors and may be her niece's firebending master. That or she lives wandering literally the rest of her life just trying to find who she really is without having to be the Princess of the Fire Nation and no longer having the choking weight of her father on her and being at peace with Ursa.

It is possible that, since Ursa wanted the hell out of that marriage and palace so bad, she purposefully wrote the letter to make it seem like Zuko wasn't Ozai's so that way she and Zuko could be set free because Ozai would have no choice/would hate her/this would bring dishonor on the royal family, etc. I mean I really do think Zuko is Ozai's son; he looks like him and even Azula and Zuko look related. But Ozai was also extremely paranoid and couldn't bear the possibility. I mean, nevermind that Zuko looks like him or anything. He's so paranoid, he kept the letter in the back of his mind. This is probably why Ozai disregarded Zuko, burned Zuko, disowned Zuko, told him he was lucky to be born, etc. etc. Ozai dismissed what was plainly in his face all probably because of that one letter and the events that unfolded in The Search (we really do need part 2 and 3 here).

The conflict going on inside Zuko makes sense due to his bloodlines. He is Fire Lord for the longest time, as mentioned in LoK, so obviously he didn't get the boot like you would think if he wasn't a legitimate heir.

So I think, right now since we don't have much else to go on, Ursa wrote the letter like she did purposefully, knowing that the little servant woman would read it/has been reading the other letters/would show Ozai. I think Ursa came up with a plan to get out, with Zuko, and this is what got the ball rolling. However, it obviously didn't turn out the way she was planning. Since Zuko doesn't know the backstory behind his mother yet and we, the readers, only know so much...you can see why Zuko would be like "....WHAT?!?!?!". We, the readers, get some insight to what's going on, because we get to see the flashbacks. Zuko does not. Zuko is travelling on with Aang and them, having zero idea yet about his mother's past.