A1. We say go/ come/ travel (etc.) to a place or event: go to bed; come to my house; go back to Italy; go to the back; be taken to hospital; welcome (somebody) to (a place); a journey to/ a trip to/ a visit to/ on my way to ~ etc.
A2. Compare to (for movement) and in/at (for position)
A3. Been to: We say been to (a place)
A4. We say get to (a place); But we say arrive in ~ or arrive at ~ (not arrive to); for other places (building etc.) or events, we say arrive at.
B. Home: We say go home/ come home/ get home/ arrive home/ on the way home etc. (no proposition)
C. Go into, get into ~ etc. = enter (a room/ a building/ a car etc.) With some verbs (especially go/ get/ put) we often use in (instead of into) The opposite of into is out of. (e.g. She got out of the car and went into a shop.)
C1. We usually say ‘get on/off a bus/ a train/ a plane’ (not usually get into/ out of)