I understand your query. The Indian subsidiary in both scenarios would operate as back office company for the US company.
Scenario 1: The Indian entity even though it would be cost centre, it needs to pay the taxes on Arm's length profit margin on cost (i.e. what an unrelated entity would have made the profit if it would have provided the services to another unrelated entity.). This can be determined using the benchmarking analysis under the transfer pricing regulations, which is usually around 10-20% of the operating costs. The GST would not be applicable as this would be considered as export of services under the GST law. However, you need to obtain the letter of undertaking for the same.
Scenario 2: Here as well the profits earned by the Indian entity should be benchmarked as per the Transfer pricing regulations. The GST would not be applicable here as well provided you obtain the letter of undertaking.
In both the situations, there would be tax at the rate of 25% on domestic companies plus to withdraw the amount dividend would be taxed in the hands of the parent company.
For detailed consultation, please book telephonic consultation.