Is Mount Everest currently becoming taller or shorter every year?
According to one survey using GPS mounted on a plateau below the summit, Mount Everest is increasing its height approximately 4mm each year.

As for plate techtonics, this site describes it pretty simply:


  Much like a car crashing head-on with a truck, crumpling occurred when the two continents met and the result was the creation of the Himalayan Mountains. Although the northward drift of India slowed dramatically with initial collision, the two continents have continued to converge as India slides under Asia.