Georgia is really easy to adapt if you are coming from asian or in general eastern countries, the culture and people being really close to together
Most of the people here don't mind where you come from as long as you blend in society which isn't that hard in my opinion. Looks might be a bit problematic, but nothing that can make a real problem.
About how long does it take to feel home - if you manage to get along with people here it is really easy. The country is one of the oldest in the world and the life goes slowly here, the capital itself is really small so you don't have to learn many things to feel yourself at home. One problem might be the thing that not many people know English here
As I've mentioned, as long as you respect the people - who are mostly traditional here, it does not take much for the people to like you. If you have some friends/relatives/people who you know in Georgia even better as they will help you out
