I am new to the Cloud Hybrid Model and planning to use the public cloud only when the on premise doesn't have the capacity to handle the traffic.
1) How to handle the traffic to be served from AWS public cloud? Data would be present in on premise, only the application load has to be shared between on premise and public cloud.
2) If ans for question 1 is possible, how to load balance the trafic between on premise and public cloud?
3) How the DNS is managed, on premise DNS or rout353?
You are misunderstanding what Hybrid Cloud is. If your data is in your datacenter and is served from your datacenter, then you are on-prem. In your scenario, you would need to route the Internet traffic thru AWS to on-prem which increases cost and latency. AWS, in this case, is just an expensive data pipe. This example could increase fault-tolerance if on-prem public Internet fails and you have the correct router setup for failover.
For public hybrid cloud, you locate your data and services both in cloud and on-prem. Then you can load balance, failover, etc.
For private hybrid cloud, you are combining cloud resources with your datacenter resources for consumption either in cloud or on-prem or both at the same time. You can combine private hybrid cloud with public hybrid cloud.
The answer to #2 and #3 depends on what you have deployed on-prem and in the cloud and how traffic needs to be routed, isolated and protected.
In a typical environment, you would implement redundant routers with multiple connections to the Internet and to your cloud provider. These connections provide fault tolerance and routing. There are many options for setting up DNS which depends on the details of the implementation. You can combine Route 53 with on-prem DNS with DNS forwarders.