Yes, when you pasted the design, it kept the same style. That's what we would expect. The changes you made for the style for each tool will only affect the new objects that you draw.
Instead of creating it again, you would just have to select each of the objects and raise....I think in this case it will probably be the alpha level for each color. Select an object, go to Fill and Stroke dialog, move the A slider all the way to the right, or make the value 255. That 2nd article I gave you will tell you all the places to look for transparency-related problems.
Yes, Inkscape is much more complex that it appears to be at first. I was so happy when I first started using it, because it was much easier than raster graphics (which I still find to be difficult). But the more I used it, the more I learned how much more powerful it really is. Even now, 8 years later, there is much I don't understand. But it's a super-great tool!
Happy Inkscaping!