@Santiasan
Okay, I see what's going on. You are working with low-resolution, heavily-compressed JPGs of full-color images. The very first link in your post, which is supposed to be the original image (but clearly isn't because the text has already been removed from it), is already destroyed by compression artifacts. PNG will not help, and neither will reducing the color depth to 8 bit.
First off, where do you (or the cleaner who removes the text) get the original image from? I ripped out a
page from chapter 1 hosted on Kakao which I assume to be the raw (720×1098, 66 KB), using the browser's built in Inspect Element tool. By itself, the image is already well-optimized (Kakao clearly cares about preserving bandwidth!), but since we still need to typeset it, we'll have to decide how to compress the result when we're done editing the image.
Doing so in Photoshop CS6, here's what I got by recompressing it with JPG (Save for Web... → JPEG, 80%, progressive) and running it through File Optimizer to trim off the fat:
91.2 KB. Yeah, we got a 38% size bloat, but we got it to look
nearly indistinguishable from the raw. As the original was already well-compressed with no leeway for safe size reduction, if we had tried to
match its size, we wouldn't be able to avoid
noticeable quality loss. So that's how JPG fares.
How about PNG? Since the source is full-color
and has soft color gradients, the only option to avoid major quality loss would be to
save it as 24-bit, fully preserving fidelity at the cost of bloating the size to 302 KB (a massive 358% increase!). Worth it? I think not. Reducing the color depth to 8 bit would allow us to just barely beat the 80% quality JPG's size but immediately produce
horrible color banding, so that is out of question. Even dithering won't help avoid
very noticeable grain, not to mention it would explode the filesize again in this case (131 KB). Don't bother with it. Finally, there's the unpopular option of using the lossy mode of PNG which can be accessed by e.g. checking "allow lossy optimizations" on File Optimizer's PNG tab. This way we can reduce the size by a 1/3 to
203 KB at the cost of a minor fidelity loss (which in this case, somewhat ironically, smoothened out some of the artifacts originally present in the raw). Worth it? Not at all.
Hence, use JPG with high quality settings (80–85%, optimized or progressive) for full color digital images. And don't use second-hand originals; take the raws from the source if possible. Free webtoons allow easy (if a bit tedious) extraction of images from the online reader pages.