I'm not sure if a one size fits all.  The best way to see if it works for you, is to use it or apply it to some images.  Really just see if you like working with it.   Or use it as a starting point and tweak it later.
I did this piece recently and applied your palette:


Here are some other images with your palette:


I just let Graphicsgale apply the palette for all these.

Colors are something you'll always be trying to get right as long as you remain artistic.  It's just the way it is.   

2446 colors is a lot I would say.  I do like the mistiness of this tho.

On stuff this small, I would avoid dithering as much as possible.  The single pixel thing makes it look too busy and unrealistic.
And the colors shouldn't be as saturated since they are way in the distance and usually be on a dark background.
Edit:

I can't use them horizontally because the health bar is a vial standing upright with an animation unfortunately.

Could you fit them into the bottom panel?  They seem a bit large anyway.  The bottom panel looks good and creates separation.  Right now the floating hud elements are distracting and seem lost with the other items in the game world.