Singapore Post-study work - Post-study work visa

Is there any option for a student who does not get a job within the 30-day post-study work visa period to come back to India and then apply for a job or get sponsored by an employer from abroad in New Zealand/Singapore?

Which country offers the fastest post study work path for an MS CS graduate who eventually wants to start a company?

What are the post-study work opportunities in countries like Ireland, Singapore, UK, and Japan for psychology or industrial work for a Master's?

Are there stay-back options available in countries like UAE, Malaysia, and Singapore for short-term courses for a Diploma?

Does the stay-back duration depend on whether the course is STEM or not in Singapore?

Does Singapore have a stay-back option after studies, and what is the duration?

Which other countries besides Singapore should we consider for her studies?

After masters in Singapore, will I get only three months to find a job or internship?