Aang was never formally taught the other elements, like Korra has. I think Aang had the harder journey in that regard.
Nah, when we first see Li'l Korra her reason for being so confident that she's the avatar is that she's already slinging around water, earth and fire like nobody's business.
That has no bearing on how long it took her to get in touch with her spiritual side at all, however. Korra and Aang are basically opposites: Korra's very pro-conflict and likes solving problems via force. Aang avoids conflict and prefers to just have things resolve peacefully if possible. It makes sense, then, that he more easily taps into the spiritual side of things, has mastery over the less directly combat-oriented forms of bending (air and water both came first and easiest to him as I recall) while having more difficulty with the destructive-inclined elements of earth and especially fire. Korra, on the other hand, has no problem kicking all kinds of ass with earth, water and fire, but can barely even wrap her head around the concept of avoiding
confrontation or considering alternative methods of problem-solving, blocking her completely from the spiritual side of things and the whole realm of airbending due to her all-I-have-is-a-hammer mindset.
Even when, in full panic mode, she gets access to airbending it's basically just used as a substitute for fire; she doesn't show any kind of mobility-related usage for it, which is practically the main draw of that element. Likewise, her finally getting in touch with the other avatars is solely driven by, essentially, having no choice but to do so. Like Aang tells her, she's hit rock bottom at that point, the best possible state for being open to looking for answers (or something like that, I'm paraphrasing). It took her longer to reach that point than Aang, age-wise, and still required a massively life-altering event to trigger at all. I'd hardly call that epic progress.
As for the returning bending thing, that's just Avatar stuff. I don't think we ever saw Aang failing to return someone's bending, did we? Pretty sure the whole point of Avatar state is that it teaches you all the stuff the other Avatars know/can do. It's not as though Korra spontaneously invented a technique no one had before; she just tapped into the whole Avatar do-whatever-plot-dictates-you-need-to-be-able-to-do power.