For production networks, a minimum of 3 APICs is supported and anything less is not. Anyone who wants purchase an ACI lab kit (IIRC is 1 APIC, 2 leafs, and 2 spines), then 1 APIC will work for lab/testing environments. There is configuration in the APIC which will permit a single APIC to be a single cluster.
In regards to your first question, the minimum is 3 APICs per fabric. For stretch fabric or multi-pod, these are still considered 1 ACI fabric even though they may be in different sites. For multi-site, each site is considered an ACI fabric.
With ACI, the APIC clustering is done in odd number of APIC servers (1, 3, 5, etc) to allow a majority or minority state.
Lets say you have a target cluster size of 5 APICs. At some point a failure occurs and now APICs 4 and 5 are unable to communicate with APICs 1-3. APICs 4 and 5 are able reach each other and form a healthy cluster. APICs 1-3 are able to cluster together without APICs 4 and 5. You're now in a situation where there are 2 different APIC clusters are in conflict and the switches need to know which APIC cluster should they receive any new policy from. This is where the split brain condition comes in. APICs 1-3 would be considered in majority state (3 out of 5) whereas APICs 4-5 are in minority state (2 out of 5). In any case where APICs are in minority state, they cannot create new policies and make changes. Anytime there is a majority cluster, then changes are safe to make.
More info about split brain here: https://aci-troubleshooting-book.readthedocs.io/en/latest/apic.html#majority-and-minority-handling-clustering-split-brains
-JW
