The word "home" can be a noun, an adjective, an adverb or even a verb in some cases. This would depend on the context in which you are using the word. "Home" as a noun- example: the floods forced many people to flee their homes. "Home" as an adjective- example: I don't have your home address. "Home" as an adverb- example: what time did you get home last night? "Home" as a verb- in this case you would not use the word home but rather homing which is derived from the word home. Example-more tan a dozen of chicken were homing to their chicken coop. As you can see, the word "home" can be used in a variety of ways and the context of the sentence will determine wither it is a noun, verb, adjective or adverb. In your example, the use of the word "home" in "on the way to home" is used as an adverb which is indicating direction. However, usually people will exclude unnecessary words so you could say "on my way home" or "on the way home" this would depend on the context. Including the word "to" in your sentence is not grammatically correct. But it is nonetheless an excellent attempt. Well done and keep up the good work! If you require any additional assistance, please do not hesitate to message me or book a lesson and I will be happy to help you improve your English. I am a native English speaker and a professional English teacher.

“ on my way home” is grammatically correct and home here is a noun.