How a fresh auto-scaling launched instance is registered with the ELB automatically? I know we will give the load balancer name while creating the auto-scaling group; I need to know the real 'how'.
My guess is it makes an API call RegisterInstancesWithLoadBalancer. You can do that too in your own code. It does not have to be through Auto Scaling
Can we have multiple private IPs of instances run different applications and all of them visible to ELB?
Well, ELB does not care about the ip address at all. It goes by the Instance Id. Unless it is on a VPC and uses ENI. However, ELB routes traffic only to ip address attached to eth0
Update:
Note:
When you register a multi-homed instance (an instance that has an elastic network interface (ENI) attached) with your load balancer, the load balancer will route traffic to the primary IP address of the instance (eth0).
Source: ELB Developer Guide