I can select unanswered questions with a particular tag.
How do I then select from those, the questions asked within the last 2 years, ordered by votes? Is there a way to do that?
(edited to incorporate amoeba's suggested improvement of my answer)
Within CV you can pretty much get what you seek, for example
i. you can easily get all but one of the things you seek, for example if you type
[nonparametric] answers:0 into the search box and click the "recent" tab you get this search, which is the most recent questions in the nonparametric tag with no answers. This uses only options you can see by clicking on "Advanced Search tips".
ii. if instead you put in the search box
[nonparametric] answers:0 created:2y.. (you need the two dots, see below*) and select the "votes" tab ... you get this search (you can find this option by scrolling to the bottom of the Advanced Search tips" revealed in the first suggestion and clicking the link there, which lists even more options). [[This seems to be pretty much what you asked for.]
Outside of the usual CV pages, another way to get what you want (but which allows you to filter in ways you can't within the usual search interface) would be via a data.SE query
* If you omit the dots after "2y" you get questions which have no answers, posted in the calendar year 2015, sorted by votes.