the colour picker is on the Colour Panel … you will have to click the eye dropper symbol and drag it to the area of your image you want to sample. To send the sampled colour to the colour well left to the eye picker (which usually means to apply the colour), you then will have to click the little circle right to the eye dropper.
When you are using a brush, you can also simply hold down the Option (Alt) key and move the mouse a bit, to sample the colour an area of your image.
Finally, the Pixel Tool should allow you to add single pixel dots to your image, simply by clicking. I wonder why this does not work for you. Could you please provide more details?
