How to know if a topic is completely explored? I read a very recent paper that describes something I am only starting to study. Basically, it looks like authors of the paper have covered almost everything that can be explored in the topic.
How can I know if there is room left to research the topic? Should I approach the authors with a similar question?
Welcome! The answer is usually that the topic is not completely explored. When you're new to an area, it can be hard to see what the open questions are. Hold off on asking the authors anything until you've asked your advisor and really dug into the topic (reading related papers, working through the problems). 

There's a nice answer to this question about approaching a new field:
Exploring something completely new, even silly.

Beyond that, I encourage you to look at the Illustrated Guide to the Ph.D.
http://matt.might.net/articles/phd-school-in-pictures/