Say I have a fargate service configured with minimum of zero pods and maximum of 5.
And say on one particular day the service was never invoked and there were zero pods running the entire day. Will the cost of that Fargate service for that day be zero?
Fargate cost is based on vCPU and Memory per hour. So yes, the cost will be zero of no pods are run. See https://aws.amazon.com/fargate/pricing/.
Now EKS charge is a separate matter. Since you mentioned pods, I assume you are using EKS. EKS has its own charges per hour. See https://aws.amazon.com/eks/pricing/.