weekend and weekday formulas

Hello,
I have a problem with WEEKEND and WEEKDAY formulas. I am trying 2 different DATE formats on my sheet, but I couldn't choose the exact weekend days. I am sending some screenshots about my problem. I have tried many times, but formula takes the wrong data format and colors the weekend days differently.

Here I used one USA data format and the second is Turkish date format. You can see the dates top in the command line. Both of them selects the wrong weekend days. And some cells haven't date, it colors it too. And when I use WEEKEND and WEEKDAY formulas with input like this $D$10, it doesn't do anything. When I write it like this $D10, it colors some of them. But not right. It selects that if the date 11/03/2017, March 11, 2017. But I have tried it with Turkish date format too.

I don't understand why it is like that? Does anyone understand my problem and where did I wrong?

Thanks for your interest.