"when I resize the window, the lines all shift to the right as I drag. "
Look up "Setting auto-resize options for layout objects" in the on line help. It sounds like you have this option enabled for your objects. (It's controlled by the Object Info palette.)
I haven't had problems aligning vertical lines in the body with vertical lines in the header, but if you need to make micro adjustments to a layout object, select it and use the arrow keys to "nudge" them one pixel at a time.
You may already know this, but you can click on the units to cycle through the options from inches to centimeters to pixels. I set my units to pixels when using the Info Palette to adjust an object's size or position.
Hopefully that'll help you out.
Normally, I just turn on the left and/or right borders of a cell get vertical lines, but I know that's not always possible or ideal. Sometimes the border is too "tight" to the edge of the data and sometimes you want borders where there is no object with just the right position/size to provide the desired line.