While the home page is fine, on the subpages of my site at http://tcisoftware.com the images are not full height. See http://tcisoftware.com/our-leadership as an example.

On all pages I am using an empty row with the following parameters:

1. Row Stretch: Stretch Row
2. Full Height row: Yes checked
3. Content Position: middle
4. Parallax: Simple

1. Background Style: Image/Parallax
2. Parallax Style: Simple Background Image
3. Background Image Repeat: No repeat
4. Background Image Size: Cover – Image to be as large as possible.

All other settings are default.

This is expected behavior, the image really “covers” your row, thing is it gets cropped vertically as your rows content is smaller than the image height, it does cover the row though. If you want more of the image to be shown vertically you can add a larger padding to the content within it for example align it to top or bottom depending on what you want to be seen from the image.
More on the topic:

http://blog.vjeux.com/2013/image/css-container-and-cover.html

https://developer.mozilla.org/en-US/docs/Web/CSS/CSS_Background_and_Borders/Scaling_background_images

There’s no such thing as width and height of a full row. It depends on the user screen resolution. If you view it with a 1920×1200 for example your row will be 1920 wide and as tall as the content. On a smaller screen the full width row will obviously be narrower.
What you need to understand is how Cover background sizing works… and this explains it rather well.

http://blog.vjeux.com/2013/image/css-container-and-cover.html

If setting full width row background images I would always use 1920x … as on large screens you have to make sure it will look good and not stretched which will diminish quality.
Then you have to experiment on different screen sizes (resize the browser) what happens with the background image so that you get the wanted effect.

Well one more thing, can I set the header to the full width? Can I put the logo more left of the header and a language translation tab on the right without any padding of the header?

As for the header – yes, just like we have on our Demo landing page?

#header .container {
    width: 94%;
}
.container.mega_menu_holder {
    width: 100% !important;
}