How should I rewrite docker-compose.yaml for Kubernetes?
The short answer is yes, you can replicate what you have with docker-compose with K8s.
It depends on your infrastructure. For example if you have an external LoadBalancer in your AWS deployment, it won't be the same in your local.
You can do rolling updates (this typically works with stateless services). You can also take advantage of a GitOps type of approach.
The docker-compose notation is different from K8s so yes, you'll have to translate that to Kubernetes objects: Pods, Deployments, Secrets, ConfigMaps, Volumes, etc and for the most part the basic objects will work on any cluster, but there will always be some specific objects related to the physical characteristics of your cluster (i.e storage volumes, load balancer, etc). The Kubernetes docs are very comprehensive and are super helpful.