Here, "home" is an adverb like "away" or "out". Similarly, "here" and "there" are often used as adverbs instead of pronouns. I walked in I walked out I walked away I walked here I walked there I walked home. If you want to use "home" as a noun, you need to add an article like "the" or a possessive like my. I walked to my home I walked to her home I walked to the home of the president I walked to Abraham Lincoln's home.

One of the very few times you "run to home" is when you are playing baseball and have just left third base. If you're talking about the place where someone lives, it's "running home."

We always go home and never go to home 😊

"I'm running home to you" is correct. You run home NOT run to home.