Illustrator Novice Question - How to change the color of a graphic easily?

Question

This graphic is created by many shapes and elements. 
Two colors compose this graphic: red and white. The shapes are composed in two colors red and white in fill and stroke. Some shapes have a red stroke and a white fill. Others have a red fill and a white stroke.

I want to know how I can in one step, or in few steps can change the color of this image so that the red parts of it would become white and that the white parts of it would become transparent, so that I would be able to take this graphic, move it onto a background of any color and have it displayed in white.

I could individually select each object in the layers panel and individually change the colors of the fill and stroke but that takes an extremely long time and is an arduous job because there are so many elements (shapes) to this image! I can make an accident! Therefore I want to know how I can do this in the shortest amount of steps with the least possible room for error. 
Also, while looking through the elements in the layers panel that compose this graphic, most elements usually are seen in the image itself. However, I noticed that there are some elements (named as Path) that are not seen in the image that exist in the layers panel! These elements have an awkward color scheme as well; in an image of red and white, they have a fill and stroke color scheme of black and gold and they are nowhere to be seen! When the element is selected in the layers panel usually a golden path is just shown on top of the image. What exactly are these elements? Since they do not have a visible presence in the image itself, do I have to change the fill and stroke of these elements as well, in order to perfectly change the color of the graphic to the colors I want?

Also another strange occurrence is that for a shape I found in layers, it is seen with a red and white stroke and fill; however in the layers panel the object is indicated to have a blue fill and transparent stroke! Why is this so? The two objects in the picture above have the blue and transparent color scheme when they are actually shown in red and white in the graphic.

Thank you all for your help.

Answer 1

First I would like to address that some of you're paths are in NO FILL & white Stoke. The Compound Shapes (Semi-Grouped) are Colored in Blue but if you click/Choose the specific or individual path it is in fact colored White.

Second If you want to color the whites to be transparent or see through You must expand their Appeance. Select all the whites (Select 1 path with color FILL&STROKE then Select>Same>Fill & Stroke. Then Expand them. As Shown

with the whites are grouped and the Red is path (eg. Red Square background) Excude them together (White on top) Pathfinder>Exclude

It will give you the all white color. The Target whites will be transparent or See through.

Answer 2

You can use the Recolor Artwork feature to easily recolor artwork without having to worry about the artwork is constructed and making selections.

Just select all your artwork and hit the Recolor Artwork button in the control bar (or go to Edit → Edit Colors → Recolor Artwork...). You can then easily change colors directly on the "Assign" tab, or adjust things like brightness and contract visually on the "Edit" tab:

That's only going to get you so far if you want to make a certain color transparent though. Assuming you have shapes that overlap etc then making them transparent is only going to show what's below...

The easy, destructive way would be to simply select all your artwork, then...

1. Expand everything (Object → Expand Appearance/Expand)
2. Hit the "Merge" Pathfinder button
3. Delete everything you want to be transparent (to make the selection easier you can select one, then go Select → Same → Fill Color)
4. Select the rest and change color as needed.

A less destructive option for creating the transparency would be to use knockout groups (as I describe here), but that would be a lot more involved and take a lot longer to make the correct selections etc. depending on how your artwork is set up.