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To be honest, those aren't really colors. A "color" tends to be one single color. They really are images. But yes, there are a couple of ways which you could use those images to fill the objects you make with Inkscape.
One way would be to use clipping. Let's say you have a circle and you want it filled with one of those. Here's how to do it with clipping.
1 - draw your circle
2 - import the image
3 - move the image behind your circle
4 - if you want the stroke of the circle to show around the image, then duplicate the circle
5 - select the new circle and the image
6 - Object menu > Clip > Set
The other way to do it is to convert the image into a pattern, and use a pattern fill. Here's how to do that.
1 - import the image
2 - Object menu > Pattern > Object to Pattern
3 - draw your circle
4 - Object menu > Fill and Stroke > Fill tab, then click the Pattern Fill button, which looks like this
5 - if you need to adjust the pattern after that, please see the manual (takes too long to type, sorry)
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Attributes-Fill-Stroke.html#Attributes-PatternsIf by "marker coloring effect" you mean something that looks like you colored something on paper with a marker.....well, you could probably get close to faking something like that with Inkscape. But it would take some time and a lot of trial and error. You could only fake it if it's ok for the marker strokes to all go the same way. I mean, if the strokes go from bottom-left to top-right, for example, they would all have to go that way. You couldn't suddenly start making strokes going vertical for example. Not in the same object anyway. You could turn it around in different objects.
And the strokes would all have to be perfectly straight. I can't think of any way to do it, so that there are arched or gently curving strokes. I suppose there might be some way to make a filter.....but I doubt it.
What I have in mind for faking an effect like that would be to create a gradient which repeats itself. A single unit of such a gradient would look like the short side, or the width of the marker stroke. I guess such a stroke would usually be darker in the middle and lighter at the edges. When you finally have the gradient right, and set it to repeat, and it's filling your shape, I would guess you'd need a little blurring.
It won't look exactly like using marker on paper. I would just be close to it. You wouldn't notice any kind of texture from the paper. It would be far better to find an image of that and use it like the other images you showed.
Just a quick comment. Inkscape is not a painting program. You might do better with a raster graphics program (which are often called paint programs). Whether they could paint with an image, I have no idea.