In British English, we'd say 'come round' rather than 'come around'. This suggests quite a short journey, the assumption being that the other person might be just (a)round the corner from you, either literally or figuratively. You wouldn't say 'come round' or 'come around' to someone located in another city or country, for example. With 'come (a)round', we're generally talking about the same neighbourhood. 'Come over' suggests that there is something that the other person needs to cross in order to reach you. This space might be very small indeed: a person in the same room as you can come over from one side of the room to the other to speak to you. You can invite someone to come over from the other side of the street, the other side of the city, or the other side of the country. It can even be another continent - you could talk about your cousins in America 'coming over' to see you. The two phrases do have the same meaning, but we have a slightly different image in our minds when we say them. They're sometimes, but not always, interchangeable. And, as you can see, 'come over' is more useful, which explains why it's also more common. I hope that helps.

Yes, but "come around" is less common. It also depends on the rest of the sentence. "Come around" also sometimes means to change one's mind to the speaker's way of thinking. (Often used in the future perfect tense)

E.g. “Why don’t you ‘come over’ to my office at 11. We’ll chat, and maybe I can persuade you to ‘come around’ to the idea that dogs are better than cats.