The correct answer is option 2 - 1 and 3 only.

Statement 1 states that the Bay of Bengal Initiative for Multi Sectoral Technical and Economic Cooperation (BIMSTEC) is an international organisation involving a group of countries in South Asia and South East Asia. This statement is correct as BIMSTEC is indeed a regional organization comprising seven countries from the Bay of Bengal region. These countries include Bangladesh, Bhutan, India, Myanmar, Nepal, Sri Lanka, and Thailand.

Statement 2 states that all countries with whom India shares an international border are members of the organization. This statement is incorrect. While some countries with whom India shares an international border, such as Nepal and Bhutan, are members of BIMSTEC, not all of them are. For example, Pakistan and China, with whom India shares international borders, are not members of BIMSTEC.

Statement 3 states that Bangladesh, India, Sri Lanka, and Thailand were the original members of the organization. This statement is correct. These four countries were the founding members of BIMSTEC when it was established in 1997. Other countries have joined subsequently.

Therefore, the correct answer is option 2 - 1 and 3 only.