The ENCODE consortium classifies human and mouse genome elements to try to answer your second question.
Work by ENCODE suggested up to 80% of the genome is functional in some way. In other words, by that upper-bound measurement, there is apparently more to DNA's role in biology than just encoding genes — there's a lot going on under the hood.
Case for ...
First, please note that the article you link is not a peer reviewed article. It is a popular, easy-to-read article.
Does this article call into question the theory of evolution?
No, it does not. What makes you think it does?
The article talks about a very old (and somewhat still ongoing) debate about the relative importance of genetic drift vs selection ...