Hi Hari,
First I have a question. What does the error say? "Invalid username or password" or "The system cannot be reached"?
There is some misunderstandings here. Certainly you can use SAP HANA Studio to connect your SAP HANA developer edition on AWS. I've successfully used SAP HANA studio to connect my SAP HANA developer edition on AWS using the public IP of EC2, instance no. 00 and SYSTEM/manager and I just tested it. It works for me.
If you don't add <public ip> imdbhdb in your hosts file, you will see a yellow triangle instead of a green square in SAP HANA studio.
Regarding your problem, I assume all of your inputs are correct, then maybe the problem is your SAP HANA server. So, my suggestion is use puttygen and putty to login EC2 (ssh, OS level) and see if the SAP HANA server is started. The instance is running just means the Linux box is on.
You can follow SAP HANA Developer Edition on Amazon Web Services (AWS) to connect your EC2 using puttygen and putty.
Best regards,
Wenjun