Speaking from personal experience, adjusting to the social and business culture is taking longer than I thought it would do. It's difficult to clearly and diplomatically express why. There are some nice expats, but the community on a whole seems to be like a secret society. I try not to take it personally and I can understand if they have trust issues.
In terms of feeling at home, I'm not sure how long it will take or I ever will feel at home. Don't get me wrong, I don't regret moving to Botswana... my wife is Motswana and she's had a reverse culture shock. The key for a successful integration is get connected; it's very difficult to survive in Botswana without a reliable network. If you've relocated here through work, then you'll be fine. Just identify the good ones from the bad ones and be prepared for this process to be trial and error.