Now to go to albums I need to open camera, then click the last saved image, then click the photos icon, then click the albums icon. Can I just have the icon on my home scrern to go to albums instead? Also how about going to a specific album or even a specific photo (like a subway map or my family picture)?
Yes, you can. The "albums app" is usually called "Gallery" or "Photos", so just place an icon of it on your home screen.
Depending on launcher it may also be possible to add a shortcut to a particular image to your home screen. Also, as far as I know, ES File Explorer can do that too.