I can try to help you,
Best way to get the colors you want is to make swatches, use the swatch window. If you are printing PMS colors you can go to the upper right of the window and select open swatch library in the pull down list and add your colors there. You can also create your own colors in the pull down window. Select new swatch. Note Make sure you click global then if you edit that color it will make every item with that color change. If global is not selected it will only change in the pallet. Last thing is if you have two colors in the swatch library and you do not want the one color anymore and want it to change to the other color, put them next to each other in your swatch library and hold shift and select the color you want to keep first then the color you want to get rid of second then under the drop down in the upper right select merge swatches. The color you want stays and everything that was that other color changes.
For the color picker the item you want to change to a new color needs to be selected. So if you have a box on an image you want to change you have to have the box selected then use the color picker.
Gradients are completely different in Illustrator so I always go back to Photoshop for that.
You have some options but you have to really know illustrator to use them and if you are printing it is always recommended to us photoshop for them.
Not sure what you are doing with the stoke effect but sound like your stroke is to big, I would have to see it to help you figure it out. Use the storke window to help you set size of stroke, sound like the default is to big a point size.
Hope this helps a little. I am not the best to explain things over text. I am more of a shower. Please excuse the typos.