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Visual Force API
What does it mean by <apex:outputText value="{!$Label.site.stay_tuned}"/>? How do I know all key and values about $Label? How to add and change those? Is there any reference website for it to see all variables? Any Visual Force API?
In answer to your more general question, take a look at this page from the VisualForce developer's guide.
All Answers
Label denotes a "Custom Label". There's two ways you can change the value of these:
1. Go to setup > Create > Custom Label on your Org and you'll see all the labels listed there.
2. Use the Force.com IDE and Meta data API to modify this in bulk.
In answer to your more general question, take a look at this page from the VisualForce developer's guide.