How to tell how far you are from checkmate? What are some tips to tell if you are close to checkmate?
It is extremely difficult to know how far you are from checkmate. If you could calculate as deep as you wanted (essentially, solve chess), then you would be able to look it up on a database. My suggestion then is that you try to calculate and see if you find a series of moves that do the job. As this series of moves will very likely proceed from a tactical motif, I strongly suggest that you study a few of the many indicators that allow you to know whether a tactical combination is possible.

As a starting point, you may want to check Chess Tempo and it's Tactical Motifs list, which include many of the most basic and important ones.