On the first one you can see the rest of the plane because maya is still shading the specular component of your shader.
Plug your alpha channel (inverted) into your specular color of your shader or if you already have a specular texture applied you can throw it on the gain of that texture (multiplying everything by 0 where you want no reflections).
Also you have some white edging on your texture because your apha channel is not correctly reaching the edges, how are you generating this alpha map?
If you paint everything on a layer in photoshop its much easier to create your transparencies. If you are just painting on white to create your color and then selecting the white areas make your transparency, be aware this is using a threshold to and might not select partially white pixels. To check the result of your transparency in photoshop, put it in a layer over your color, invert it and set the the layer to multiply this will highlight any problems.
FX supervisor - double negative