How to paste an equation to a graphics

According to the documentation, "PasteButton, evaluates its arguments in an ordinary way, so that expr is immediately evaluated"

It is like you evaluate Plot[\[SelectionPlaceholder], {x, 0, 10}] which will give empty plot.

This could be one solution:

PasteButton["Plot", Defer[Plot[\[SelectionPlaceholder], {x, 0, 10}]]]

In case you want to plot in place you can use something like:

Button["Plot", 
   NotebookWrite[ 
      InputNotebook[],  
      ToBoxes @ Plot[ 
         Evaluate @ ToExpression @ CurrentValue @ "SelectionData", 
         {x, 0, 10}
      ]
   ]
]

You may want to add Method -> "Queued" for more complicated plot to avoid timeout.

And if you want x from the selection to be scoped properly, e.g. to give a plot even if x already has a value, then wrap the procedure inside the Button with Block[{x},...].