Explanation:

To determine which statements regarding the India-ASEAN start-up festival proposed by PM Narendra Modi on October 28, 2021, are correct, we can analyze each statement:

1. The festival was announced as a part of friendship year celebration between India & ASEAN in the year 2022. - This statement is correct as the India-ASEAN friendship year was celebrated in 2022.

2. ASEAN approval for reviewing FTA is important for India to address the problem of non-tariff barriers that Indian businesses face. - This statement is also correct. The review of the Free Trade Agreement (FTA) with ASEAN can help address non-tariff barriers that hinder trade.

3. India’s trade deficit with ASEAN region has widened since 2010, when FTA was implemented. - This statement is correct as well; India's trade deficit with ASEAN countries has indeed widened over the years since the FTA came into effect.

4. All are correct. - Given that all the individual statements are correct, this statement is also correct.

Thus, the answer is Option 4: All are correct.