Where can I find samples of position papers?
How much evidence for the position is normally provided?

As much as possible, actually. In a position paper, you might want to develop an hypothesis that matches previously made findings. Or you might argue that past empirical research has got its results wrong in some way because of an unaccounted for measurement or protocol error. Or you might want to make a theoretical argument, or take multiple findings from existing papers and try to explain a connection between them. If you have an hypothesis which sounds plausible (as in consistent with correctly-made empirical observations and with at least one family of theories) and you find that you need some additional research before you can confirm or reject it, a position paper is a great way to expose it.

What kinds of questions are reasonable to leave unanswered?

The ones that need a costly / difficult proof. You want to expose an opinion or idea so you get feedback on it or potential collaborators.

How long are they?

It depends on your field. In computer science, they're usually short papers in conferences or full papers in workshops.

What level of counter-argument should be included?

I'm not sure I get this question. If you know about evidence that contradicts your hypothesis, include it, and explain why you think the evidence can be neglected.

Where to look for position papers?

Go to your favourite academic search engine and make a search on papers that contain "position paper" in their title. Also, look up all recent workshops in your specific field (those you'd submit your position paper to).