'To have [someone] over' is to have someone at your place for some amount of time. It is the same principle of verbs such as 'to stop over' and 'to invite over'. 'To go out' is to go outside to do some activity. So, they're probably basically asking you if you'd rather have someone at your place, keeping you company, or get out of your place to meet up with them.

Yeah, it's just asking whether you're more likely to invite your friends over to your house/dorm/apartment, or are you more likely to meet them somewhere else

Do you like having company over ( meaning : Do you like people coming to your house) or do you prefer going out ( meaning: do you like to go to a restaurant, park, movies, ect [Could be with a friend or not].