DNS Infrastructure Architecture Assistants

Hello:

I am wanting to deploy our own DNS infrastructure and would like assistance and advice on the best way to build and deploy the system.

We will be using multiple cloud vendors such as Linode, Vultr, Upcloud, and Digital Ocean so zone requests are served from the closest node.

We will be using 4 nameservers.
ns1.example.com
ns2.example.com
ns3.example.com
ns4.example.com

My questions are:

1)
I guess each nameserver can use one IP from multiple providers. So if one IP is unreachable for any reason the nameserver remains online and serving requests?
Example:
ns1.example.com
54.40.175.25 (Vultr)
162.200.201.25 (Linode)
45.22.58.77(Digital Ocean)

2)
When you configure nameservers do you have to configure all 4 nameservers in each geographic location using an IP from that location so requests are served from that location? Or do you configure ns1 for example in USA, ns2 in Europe, ns3 in Asia, etc.?

3)
How do anycast IPs work? Should we consider using anycast IPs?

We would like your expertise in designing a fast redundant, failover system.