The first one The back ground was a texture of some sort, and the used a lighting filter on it the has the three spot lights the shapes are most likely done using the vector shape tool in the shapes menu under custom shapes (the star shape) the circle on the outside edge is another shape, the shapes are then turned into selections and by the looks of it was free hand air brushed or a gradient was used on the selection to give you the color variations (gradient tool is under the bucket tool in the tool bar) click on the little triangle at the bottom right of the bucket icon to expand the menu, the line art for the person and rabbits maybe done with the pen tool, then maybe stroked with one of the calligraphic brushes selected and turned on in the paths menu then for part of that a selection was made and the gradient tool was used, you could also do this with layer masks and adjustment layers. Hard to say for certain what method was actually used, or if this was even done in photoshop may have been photoshop and Illustrator, or some other program.
Second one may have been done with a simple hard round default brush set at something between 40 to 70% opacity level and the figures sketched out, then the rest filled in with a texture brush of some sort, set at various opacity levels, there are stock brushes that will do this
no problem The first one looks like it's done with a stock pastel or dry media brushes in photoshop you can find them in the brush menu by clicking window brushes or hotkey f5 and clicking the the small triangle top right corner, load up the different groups and check them out dry media, natural, basic and assorted would have something similar then just adjust your size and spacing in the brush menu a long with your opacity settings to get the look your after this look can be done easy enough. The second one looks like it was done with the watercolor textured surface brush or something close to it, you can find it under the wet media brush in the brush menu they just adjusted size and the opacity levels as needed you can find that at the top menu bar when you have the brush tool selected hope that helps, feel free to ask anything else if it's not clear do my best to help out
Well, it's not a question about software but about style... they have a "cartoon" style, so the key word is stylization, so, when you practice, you need to turn the elements in geometrical figures... like the nose here: [link] it's like a simple curved line. Of course you can't copy others' style because everyone has got his own, but you can exercise on others' works just to make you an idea of the stylized anatomy. About photoshop, I think that you can start drawing on paper using a pen or hard pencils to highlight the lines and then, if you want to adjust your work on the computer, you can use the vectors of photoshop and the result would be more like the first style of drawings that you linked here.
I hope I helped you a little and I hope I got the point of your question!