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I'm not really sugarcoating things here, so sorry if I offend you. If you get upset while reading this, then keep in mind that I spent over an hour thinking of and writing this. I'm not trying to offend you or hint something like "Give up! I've never seen anything so horrible before!" This is just for the sake of your improvement.

---Story---
We start with a tax collector complaining to them or something? It's hard to tell what's going on here (mostly because of the art). The parents (?) step outside and they're apparently dead in a few moments.

"The two of them are lying on the ground, there's no trace of any other beings having been in the area... Oh my god, they must be dead! Yup, no denying it. I think I'll go die now. There's no point risking my life to see if they're still alive or not; I'll just end it right now."
She didn't even cry. The suicide attempt was pretty half-assed... Choosing to kill yourself isn't quite that easy. Why did the character even consider suicide at that point? The idea behind suicide is to run away from your problems. Maybe you'll be in debt for life, maybe the loved one who gave meaning to your life is dead, maybe some people turn everyday into a living hell... When you're in a situation like that, where can you run to? You can't simply forget the problem since it's always right in your face. It seems like the only way to run from the problem is to kill yourself - a coward's way out, or a smart person's way out if they're 100% positive the rest of their life will be torture. But Kousuke gains the will to live so suddenly just by seeing a book on the floor...

The joke about the names starting with the same sound reminds me of a certain moment in InuYasha... and if you want to use Japanese humour, Japanese names, and have the panels read right to left... Well, that joke wouldn't really make sense in Japanese. The Japanese language doesn't have a "k" - they have "ka, ki, ku, ke, ko" (same idea with all of their consonants). If I remember InuYasha right, Ayame was complaining at Kagome because their names both end with "me". Anyhow, the joke wouldn't fly well with "ku" and "ko" since those are considered two different sounds in Japanese.
I would recommend avoiding Japanese humour/style unless you're serious about Japanese. I mean, you can still go ahead and do manga, but I would recommend using English names, settings, clothing, puns, and so on. I know Japanese is tempting, especially after seeing so much anime, reading so much manga, or listening to so much Japanese music... I tried to make a manga before with a setting similar to InuYasha. It was Feudal Japan, I was trying to dress the characters up as if they were from Japan, and I'd stick a cherry blossom tree in here and there. Trust me, it doesn't turn out well. As Kupocake said, try to stick to things you're familiar with. The only martial art I've trained in is taekwondo, and I've been thinking about making a manga based on it - it would be a bad idea for me to do one about karate or kung fu since I know nothing about those martial arts. I've also considered school life manga. I've decided that I'll do it based on Canadian school life since that's what I grew up with - if I do school life manga, it won't be in a Japanese school with Japanese school uniforms and bento/lunch boxes. I've seen that a ton in anime, but I only know what the anime has shown me - I don't truly know that setting.

The giant boomerang certainly made me think of Sango from InuYasha, but there were two boomerangs instead of one, and I figured "Well, would it be so wrong for another story to have a similar weapon? Jakotsu (from InuYasha) has a whip sword thing... So does Ivy (from Soul Calibur), Van (from Gun X Sword), and probably other characters from other things, though their whip swords are different in their own ways."
I don't watch "Avatar: The Last Airbender", so I wouldn't know about that part Kupocake mentioned... I think I saw half an episode once, and I think they manipulate the elements somehow. Final Fantasy Tactics has a "geomancer" class that manipulates elements, so that much isn't unique to Avatar.

The "four elements" thing seems sorta typical, but you are using seasons instead of "wind, water, fire, earth" (alternatively, one of those might be swapped with "lightning"). You just gave the main character "wind", though...

Why is Kuro following Kousuke?

The guy who stole the book... Well, it sounds like he knew about the book beforehand and that he might have been the one to kill the main character's associates. And yet he's willing to play a little game for it? Why doesn't he just run off?

"Meet me at Troll Mountain"? Aren't they already at the mountains?

---Art---
I think the paneling looks wrong... What I do is start with a nice rectangle on the page, then I draw lines from one end to the other to divide it. The way you have boxes placed around leaving white spaces in random places looks unattractive. In most cases, their edges should be in line with the panels around them. Here are some other general tips to keep in mind:
-The panels help tell the reader which way to read.
-If the reader is supposed to be reading horizontally, then leave small spaces inbetween the panels horizontally, then leave a bigger space when you start the next row of panels.
-Use big panels for important things.

The tax collector or whatever... You can hardly tell if it's a member of the family or not. The background should show that they're standing outside of the front door.

There are pretty much no backgrounds... the background is just as important as the characters/main focus of the picture. It tells us the setting, mood, information about the characters, and other things.

Page 3 and page 5 use the same picture...
There's one very important thing to keep in mind when you're doing manga - you're telling the story through pictures, not words. If you want to tell it through words, write a novel instead. You have to let the pictures tell the story and the writing should be kept to a minimum.
Because the pictures are running the show, you have to make them interesting. Avoid recycling as much as you can.

It's hard to tell those two died... There's no blood, the angle makes it look like they're standing up (especially since Kousuke just looked out the window and spotted them so easily)... Again, the lack of background is a problem. Are they lying on the floor? Getting angry at someone in front of them? Yawning and thinking? Hanging onto a rope? Flying through the sky? There's just no telling...

Kousuke's room is HUGE. It's like a warehouse in there. You're zoomed out so far and you don't even have anything to show us... you should only show us what you've got to show. And we see the entire room - there are no books and knife placed like in the panel below.

Just how deep is Kousuke's wound? She doesn't seem to care about it at all, but it sure is bleeding a lot. The wound also looks... I dunno, not like blood. The rip in the clothes also does a disappearing act most of the time. The shape of the blood is also changing... that doesn't make sense.

Page 10 and 20... consistency issues with the background. I know it's a pain, I've had to redo tons of things in the past since I wasn't paying attention... Consistency makes a difference, though.

Page 22, I thought Kousuke was going to light the book on fire... it's not very clear that she's combining the fire and wind ability.

What is this mountain range? Why are we shown the world map?

Page 26, why was an ocean screentone used? Most of the screentones just seem pretty out of place, really... or they're inappropriately used to replace backgrounds.

The art just needs some serious work overall, sorry. I used to find it hard to look at something I drew and not be proud of it, but you have to face reality and compare it to a professional manga's art. The difference should be pretty clear... what you want to do is try to close that skill gap as much as you can. I'm no artistic genius, myself, but here's a list of some quick tips I made: http://cloudflash.net/arttips.php