they are not GFI protected. Your electrician will need to put a GFI breaker in the breaker box. From the dimension you gave, you would be trimming these down about 1/2 inch. People have done this before with no problem and if your electrician feels confident doing it you may but, you void the warranty on the power strips.

you can order them in custom lengths to be exactly that size but there is a thirty dollar up charge for customizing and custom orders need be ordered via telephone.

The cabinet bottom isn't flush, can the strips be installed on the recessed wood under the cabinet not the top of the back splash?

Yes they can.

Can you tell me exactly how far end the 1/2 opening is for the feed wire? Or can it be feed at multiple locations along its length.

They are located 1 1/2 inches in from both ends and centered up and down unless they are a 9 inch, 12 inch or 18 inch APT series which are either left or right hand wire entry. They only have them on the end you must specify, either left or right as if they were installed under the cabinet.