My I-130 was approved...so what is next?

This page: http://travel.state.gov/content/visas/english/fees/reciprocity-by-country/UG.html explains how your husband gets his police certificate. If you don't hear from NVC for a while you can wake them up with an email to nvcinquiry@state.gov giving your USCIS receipt number in the subject line, then your name and the beneficiary name and date of birth in the text - as well as asking them to send you the NVC case number and invoice. They love working through email. You will pay their fees, your husband will fill out the immigrant form online, and you will submit to them in the US the affidavit of support and the required (COPIES of) the civil documents. Older paperwork says originals. Make sure you get the affidavit and the documents perfect. They will keep asking and wasting your time until you do. And make sure you have firm plans for your return to the US. That is key. Good luck to you both.

Wait until receiving the detailed instructions package from NVC, within 60-90 days from now which will contain step-by-step instructions of what lies ahead and how to go about it.
1. Yes everything will ultimately be handled by Nairobi, once you provide the NVC all the documents they'll ask for, including the Form I-864 Affidavit of Support. Note that there is no way in the world husband will be granted his immigrant visa until and unless you'll convince the consul in Nairobi of your intent (and having taken affirmative steps) to return to live in the US.
2. Will be explained in the NVC package - that he has a clean record in every country he lived since the age of 16.

The process is complicated and you need to hire an immigration attorney. That would be your next project.