eishiya is right. Your main tool for building atmosphere is good use of light and shadow, worry about them colors later.

Here's a four color monochrome to illustrate:

There's your answer. Your original colors perfectly communicates what you want to achieve. People always comment on colors when they have nothing to say because it is the most subjective element.

People comment on what they see, and it's down to the artist to clarify it if he wants critique to take other considerations, like inspirations or intent, into account. We all have different frames of reference after all

Here's some ideas building on MysteryMeat's edit. It's easier to work with less colors so if you can shave the palette down, go for it.

EDIT: Tweaked some more.


Progress:

In my opinion people who say try them all are right, because it really *is* down to personal preference more than anything else.

- Is there some tool that I missed that can do both tilemaps and animations?

Not that I know of. ProMotion seems like the best bet for this.

- What tool do you personally choose and why?

GraphicsGale and Gimp. I do a lot of animating and GraphicsGale is good with that. Selection tools are kinda shaky tho so I'll copy stuff back and forth between GG and Gimp sometimes when I need to.

- Am I approaching the wrong way? On one hand I feel that the tool should do as much as possible, but at the same time pixel art is a lot about precision, and maybe having advanced shading tools like in Pro Motion can actually hurt me in terms of producing less quality art?

3D is a very technical discipline so the tools matter a lot there. Vector stuff and 2D illustration less so. With pixel art the tools hardly matter at all as long as you're comfortable with them. I mean, you place a pixel and there it is! To get that pixel to work well with all the other pixels you place is entirely up to you.

- Is it wise to do tilemaps in tools like Photoshop which don't have any support for them, and just manually copy them over all the time? I've seen a lot of people do it, but I've also seen people post ridiculous workflows when they copy things back and forth between tools all the time.

ProMotion has specialized tilemap tools if I remember right. Other than that I don't know, I don't really do tilemaps myself.

Why not pick a program that looks promising and then, if or when you hit some kind of wall then try another and see if that works better for you? To me, it seems more intuitive to experiment and figure out the optimal workflow for yourself rather than try and nail it down beforehand. Everybody different and all that. Even in the 3D world where tools really do matter, people will swear by different things.