Why cant I use the width tool ?

that might be happened by clicking with the live paint bucket tool ( shortcut : K ), whenever you finish using the paint bucket tool, click on expand to convert to individual path

Here is a screenshot

I hope it will help.

your screenshot show that you are using Live paint, you need to expand the live paint by clicking on the Expand button

you need to activate the path, the anchor points show that the object is not selected completely 

click on the small little circle next to the path in the layer panel