minikube : not able to connect a locally deployed nginx service

1) Is node 127.0.0.1 my local development machine? This has got me confused me the most.

When a node registers, you provide the IP or name to register with. By default, the node is just registering 127.0.0.1. This is referencing your VM running linux, not your host machine.

2) Is my following understanding correct: The cluster (nodes, kubernetes API server) has internal IP addresses in 10.0.0.x and their corresponding external IP addresses are 192.168.99.x. The 2 pods will then have IPs in the range like 10.0.1.x and 10.0.2.x ?

Yup, the 10.0.0.x network is your overlay network. The 192.168.99.x are your "public" addresses which are visible outside of the cluster.

3) Why is the external IP for the services not there? Not even, for the kubernetes service. Isn't the 192.168.99.43 an external IP here?

The external IP is typically used to ingress traffic via a specific IP. The kubernetes service is using a clusterIP service type which means it's only visible to the internal cluster.

4) Most importantly, how do I connect to the nginx service from my laptop?

The easiest way to view your nginx service is to make it type NodePort, then deploy the service. After that, describe the service to get the port that was assigned (or after you create it will tell you as well). Then hit the ip of your VM and provide the auto assigned NodePort.

e.g. http://192.168.99.100:30001