AFI breaking up is something I never think too much about, because it seems really unlikely to happen in the foreseeable future. I just assume most bands I follow are going to keep on going until they physically can't, and AFI has a better chance of that than most.
Beyond this interview, there have been plenty of statements made to that effect by members of the band. They're still young (yes, early 40s is young these days in an era of longer lifespans), in good shape, live a clean and healthy lifestyle, and don't get bogged down with the drama that plagues other bands. In addition, they have the freedom to work on side projects to avoid getting stale or burnt out, and have a relentless drive to progress. AFI is about the last band I would worry about splitting up.
As for work on a new album, it's common practice for them to start writing a new one once they finish touring on their current release. I've read a couple comments online that seem to suggest this means they'll be releasing something sooner rather than later, but I wouldn't jump to that conclusion. The writing process can take anything up to a year or more on its own, not factoring in everything else that goes into a full release. If I had to guess, I wouldn't expect a new AFI album until 2020 at the earliest... but I'd love to be proven wrong!