It's nice to see Mathematica used to learn/teach computer science concepts.

I just have a suggestion for wrapping up your functions into a package. Do take a look at the standard packages structure:

• https://mathematica.stackexchange.com/a/132960/12
• https://mathematica.stackexchange.com/q/29324/12

Issues with your package:

• It can't be loaded with Needs["MinHeap`"] because the package filename does not match the context name
• It creates symbols like n (and other private symbols) in the public MinHeap` context. Never export unnecessary symbols or there will be conflicts. I'm sure that trying to add some of these common symbols (n, x, etc.) to a heap will now cause trouble.
• Being["`Private`"] must have a backtick at the start too—you missed it.

Some questions:

• Why are you restricting functions like HInsert to work with assigned symbols only, and not with lists? E.g. why is it necessary to do HInsert[someSymbol, element] instead of HInset[{...}, element]?
• I didn't fully understand the role of the dcount global variable. It seems to be used for all heaps. Or is the package able to work only with a single heap?

A language for binary tree based programming is Lisp, which is based upon solely that (yet complete programs can be written using it).

Mathematica has infinite List type and evaluation of List elements as functions or data, in a way mm can do the job of Lisp albeit a little differently; not so rigidly. you have to study Lisp to know what I mean.

guide/DiscreteMathematics shows ways to create, use, traverse binary and also complex trees

Hey, I only large scale tested the functions I ended up using on the project. I didn't know AppendTo was so slow. Many thanks for the suggestions though!