Is it possible to add a graph or dashboard element or dashboard to visualforce page? Can this page be made to display in Salesforce1?
Yes it can be done. You will need to embed the dashboard in your VF page using Iframes.
<apex:iframe src="link to your dashboard" scrolling="true"/>
This is a similar question which should help you. How Can I Embed a Dashboard in Visualforce?
You can also use VF charting or google APIs and build a lot more graph/chart components to your VF page.