Yeah, I remember Painter having unusual layer behavior, with the bump mapped paints some brushes not being able to work with some layers (watercolor layers for example). I can't think of anything off the top of my head that would help, except of course the stock answer of trying something other than Painter or changing your style.
All I can really suggest with Painter is to try using different brush types and layer arrangements. The acrylics may look chalky because your canvas size is really small. I usually have my canvas no smaller than 9x12 at 300ppi (pixels per inch), which equates to 2700x3600. I'm confident that the textures that Painter uses for it's brushes is meant for art being created at that resolution. The paper texture that is making the acrylic look chalky would be more subtle compared to the rest of the image if the canvas was larger. You can then export your image and scale it down when you are ready to put it on the web somewhere.
As for the color blending, I think using a paint, like acrylic or something else, that will not blend oddly like water color does with layers.
As for the line art, I'm not sure what to suggest. I don't know if Essentials has a calligraphic brush, ink brush, or something else like that; something that will make thin lines without blending weird (so markers are probably out too).
Also, don't forget that you can edit brushes or make your own (I'm not sure if Essentials lets you do that though). You'll likely have to do this to get the effect you want. You should be able to turn off some things like texture and other settings to get the brushes to behave better. So if there's a brush that you like but isn't perfect, you should be able to modify it or create a mutant brush that'll better serve your needs.
And if you can, point us to an image that has the effect or style that you are trying to achieve. That'll help since I'm not sure exactly what effect you are trying to achieve in your work, and if it's the process or software that's falling short.