Result so far:
Two Gradient textures with Constant ColorRamps added by Math node, one is rotated by 180 degrees. I can control line width by changing position of second color input in ColorRamps (they must be the same value in both).
This is wrapped in a Node Group called "Line".
Four copies of above Node Group, each of them with different Z axis rotation (0, 90, 45, -45).
It seems to be complete solution but first of all it's kind a over complicated for my taste. It's working only with Texture Coordinates > Object and controlling width and line smoothness isn't to easy.
As much as I want to ask only one question they are too dependable of each other and answering one will eliminate the need for others.
1. How to make line width control easier? (I've tried with Wave but lines are crossing after scaling.) - Partially solved thanks to @kilbee.
2. How to control line smoothness?
Thanks to @kilbee I have managed to pack node setup and control width but I have lost ability to smooth lines. I was wrong saying that one question will solve the other one:)
Blend file with @killbee setup:
I have also edited question a little bit to be more specific.
@kilbee has done it. Amazing. Here is his version packed in Node Groups with little modifications (just Multiply nodes as Values):