'The road home' is correct. Why? Because 'home' is an adverb, and its meaning includes the concept of movement towards that place - so it doesn't need 'to'. For example, 'go home' 'come home' 'return home' 'the way home' 'the journey home', and so on.

Number 1 only. "Home" is often used without an article or preposition e.g. go home, get home, on my way home, leave home. In these phrases, "home" is the place where the speaker lives but the precise place or building is not important. When "home" is used with this meaning, it is wrong to use a preposition and/or article. If you wanted to refer more specifically to the building where you lived, you would normally use a preposition plus a possessive pronoun e.g. the road to my home.....

The road home :) Eg 'The road home was long' 'We began the road home'