Can I use lightning design in my existing vf pages. Based on salesforce trailhead I can see it uses most of the CSS like tag, but in my vf page I have visualforce tag which I believe as of now not supported by lightning design.
Yes, you can use Lightning Design System in your existing Visualforce by including SLDS CSS in your VF page as a static resource. It won't affect any other styling which you've done till now.
You can download Lightning Design System from https://www.lightningdesignsystem.com/downloads/
Yup, you can use Lightning Design System in your existing Visualforce pages.
I wrote a blog post on Getting Started with Lightning Design System for Visualforce.
I hope it helps, thanks :)