As I've said, right now, Katara's feelings for Zuko are between mad and hate, while Zuko is trying to be friends with everyone at most. However, the potential to turn this into love exists, here's why:

Zuko- Zuko clearly holds Katara in higher regards than the others. Not just because she's threatened him, though. He's held her in higher regards since season one. At everyone else who has pissed him off, he's yelled at them and even threatened them at times. Sokka, Iroh, Aang, his crew, Azula, Mai, Ty Lee, you see where I'm going with this. However, the worst he has ever said to Katara was calling her a "little peasant" and he did it in a rather calm voice. Even in TFM, he snapped at Aang, right in front of Katara for his comment about dragons, but he didn't snap at her for her insults towards him. There's also the fact that he let her touch his scar in CoD, which is a big issue for him.

Katara- If you watch Katara's pattern of behavior towards Jet in Ba Sing Se, you'll see that it's a less extreme version of her behavior towards Zuko. Attack, trust via necessity, warning him that she still doesn't trust him 100%, and offensive sarcasm towards him. Now, one might say that all this shows is how she treats guys who broke her heart and that she did feel love towards him at CoD. However, there was one thing I noticed recently that's been bothering me.

In WAT, when Zuko first greets them and Katara smacks him down with water, she says, "Get out and don't come back! And if we ever see you again...

*Pauses and looks down*

"...Well, we better not see you again!"

It made me raise an eyebrow. After all, how hard is it to tell a hated enemy that, if you ever see him again, you'll kill/maim/end/destroy/some-synonym-of-seriously-hurt him? I think it shows that Katara still has something for him.

Now, you may wonder how she can then threaten him at the end of that episode and you're right, it doesn't make sense. If she could so easily threaten him after the group accepted him and he saved them from Combustion Man, why couldn't she threaten him before those things happened?

Now, as I said, for now, it's not love. But the potential for it is there within the characters. However, there is an even more important reason for it within the plot.

First off, the leaked sketch from the Boiling Rock clearly showed Mai and Zuko talking in non-favorable terms. They weren't exactly all over each other and happy to see the other one. I think they are going to break up during that episode.

Second, Aang needs a reason to let go of Katara so he can use the AS. Her being in love with someone else gives him a reason to do that. Basically, the Zuko + Katara relationship advances the plot by helping Aang grow as a character and achieve the power that he needs to fight Ozi.

As far as the gate things go, more things than Naruto and AtLA use them. I've heard them called gates, chakuras, energies, and a lot of other things. It's all blended together.