Running K8S on other environments isn't a difficult job, but you do need a certain level of experience running systems. You need to set up EtcD, in prod you have 3 or 5 of them - there are a couple of topologies for running EtcD and peer discovery (you will need to RTFM). This is all your K8S state, so you need to set up backups for these.

Each node you are going to include in your cluster needs to have docker and kubelet running. You will need to start kubelet with your init system (systemd, etc).

Then all you need is to bootstrap a control plane. The control plane has 3 components. The API server needs to communicate to etcd, everything else just talks to the API server. The API server is stateless and can (should) have multiple instances running. The other two parts are the Controller and Scheduler. Also stateless. The tool Bootkube[1] can generate all the configuration and perform the bootstrapping for you.

To answer your dot points, all but 4 are easy enough with using the kubernetes docs and some systems/networking knowledge. Point 4, assuming you mean starting new machines based on load, will require you to look at which systems are supported by the autoscaling system and potentially add an integration for your environment. There is the horizontal pod autoscaler that will run more of your service when needed and the cluster autoscaler[2] which will start more machines when it can't run as more instances of your service on the current number of machines.

Edit: There are also tools like Patroni, Stolon, and postgres operators that will assist with your DB (postgres in this case) management. Scaling, HA, backups, etc.

1 - https://github.com/kubernetes-incubator/bootkube

2 - https://github.com/kubernetes/autoscaler/blob/master/cluster...