Hello Tanul
Let me try to answer your questions below:
1 - As per https://learn.microsoft.com/en-us/azure/aks/use-system-pools?tabs=azure-cli, it is recommended to have at least system node pool dedicated for system components and a user node pool for application workload. So the answer is at least two node pools.
2 - Labels and/or taints/tolerations can be used to separate system and application workload. The same link from the above should be read for more details. The number of nodes depends on your workload, and you should assess this based on how intensive your application(s) are. As per that link, "If you run a single system node pool for your AKS cluster in a production environment, we recommend you use at least three nodes for the node pool."
3 - You should not delete the default load balancer (called "kubernetes") that the AKS cluster creates. That is not supported and will bring your AKS cluster into an unsupported scenario. If you don't want to have the Load Balancer, you should use UDR outbound type. More details: https://learn.microsoft.com/en-us/azure/aks/egress-udr
4 - Yes, each node pool can have different SKU sizes or the same size. There is no restriction here.
5 - The details provided are not enough to provide an opinion of Azure CNI or Kubenet should be used. I would recommend you reading the below to understand what is best for you:
https://learn.microsoft.com/en-us/azure/aks/concepts-network#kubenet-basic-networking
https://learn.microsoft.com/en-us/azure/aks/configure-kubenet
https://learn.microsoft.com/en-us/azure/aks/configure-azure-cni
6 - Yes, you should contact the CSAM to assign a Cloud Solution Architect, if available as per your contract.
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Thank you!