Let's start with the UVs.
On the bottom left of the UV Editor you will see... what you see in the picture bellow
Make sure the icon on the left is pressed (if you don't do that the UVs will collaps in a single line), select the UVs that you weant to offset and then enter the value 1 in the U or V area. Press enter. The value will reset back to 0.0 and the UVs will offset by 1 left or down... depending on the axis you've chosen. This is just to m ake sure that the UVs are exacly where they should. Another method would be moveing them by hand... but you could miss a few pixels this way
For your second problem... I can't tell what it is wrong with it. Tell me more about what I'm seeing there
