1. Running your own DNS is good if you need control from a control panel like cpanel, plesk etc. These applications automatically add dns records when you add new domains/users, and also sets up email. If you don't have any need to add your own records a lot then there's no point in running your own DNS.
2. I have found namecheaps, godaddys and other registrars dns servers to be highly reliable and fast, so I would recommend using them. The cons is that some of them do not support a wide variety of record types (like AAAA ipv6 records)
3. These usually support AAAA records but stuff like freedns might not always be stable. I know everydns is stable though.
All in all, I try to use my registrars dns, which is usually namecheap or netsol, and they are highly stable and nice. Namecheaps dns service is the best! They also now have Freedns, so you can use domains from other registrars!