Why do other sugars melt whereas sucrose decomposes?
You're mostly right.  Sucrose is a disaccharide composed of glucose and fructose.



It is a crystalline material.  Heating sucrose results in a complex thermal process that involves both melting and decomposition.  Depending how fast you heat it, you will observe different things.  Basically, sucrose will start to decompose when it starts to melt.  If there is some water present during the heating process, then a reaction known as sucrose inversion will occur and the sucrose will break down into its components, one molecule of glucose and one molecule of fructose.  

However if dry sucrose is heated to its melting \ decomposition point, then more complex things happen.  Significant amounts of glucose are initially detected.  Continued heating leads to "caramelization".  Caramelization is a condensation process where water is eliminated from sucrose; the initial loss of water is followed by isomerization and polymerization.  Over 4,000 products are thought to be formed during caramelization.  When this complex mixture is cooled, it is no longer sucrose.