Polymer is based on Web Components, which are an upcoming Standard. Web Component performance might depend on the use case, but personally I think (without testing it) that native stuff is usually really fast. As far as I know, Web Components render directly to the DOM, as they are just HTML.

Now for the interesting part: How does Polymer fare against React? The answer: You cannot compare them. They solve different problems. Facebook states that in their docs:

Trying to compare and contrast React with WebComponents inevitably results in specious conclusions, because the two libraries are built to solve different problems. WebComponents provide strong encapsulation for reusable components, while React provides a declarative library that keeps the DOM in sync with your data. The two goals are complementary; engineers can mix-and-match the technologies. As a developer, you are free to use React in your WebComponents, or to use WebComponents in React, or both.

So it is really not against each other, but a completely different focus and they can be used together in one project, depending on your needs!

• You can write vanilla JS components without any Polymer or React right now. You can use custom tags, templates today without any problem. If you want callbacks such as the one called when your component inserted into DOM, only in that case you will need a library like Polymer since Web Components and especially the way of creating a custom elements is far away from being accepted as a final spec. Polymer itself is also a huge codebase of JS which is not needed.
• Web Components don't have VirtualDOM. It is not needed at all. Only React invented this extra layer and overmarketed this myth. There is NO real world poblem with DOM. Why do you need vDOM and do an extra expensive operation (diff) every time? Nobody can answer. Can you?
• vanilla JS always was, is and always will be fastest optiom from perfomance and each else point of view.

P.S. never think about micromicroperfomance until you have a billion business with global infrastracture and 10+ years of history. You WILL NOT HAVE any problems in DOM perfomance without using a React.