Nouns:
* Homecoming: A return to one's home or a special event celebrating the return of former students or residents.
* Homestead: A house and its surrounding land, especially a farm.
* Homebody: A person who enjoys staying at home.
* Homemade: Made at home.
* Homeowner: A person who owns a house.
* Homelessness: The state of having no home.
Adjectives:
* Homegrown: Grown at home.
* Homemade: Made at home.
Verbs:
* Homestead: To establish a home or farm on land.
Phrases:
* Stay at home: To remain in one's residence.
* Go home: To return to one's residence.
Other:
* Home-cooked: Cooked at home.
* Home-based: Based at home.
* Home-schooling: Teaching children at home.
This is not an exhaustive list, but it gives you a good starting point for finding compound words with "home."