After course completion and expenses, can I do any business or is it only job-related in UK/Ireland for a PhD?

It depends on the country:

- UK: Yes, after your studies, the Graduate Visa allows you to work in any job, be self-employed, or start your own business for up to 2 years (3 years for PhD graduates). Other visas, like the Skilled Worker Visa, do not permit self-employment or starting a business.
- Ireland: The post-study work visa (Third Level Graduate Scheme) lets you work for up to 2 years, but you cannot start a business on this visa. Starting a business requires a separate entrepreneur visa.
- UAE: The post-study work visa allows you to work for up to 2 years, but starting a business requires a separate permit or trade license.

If you want to start a business after graduation, you will need to apply for the appropriate business or entrepreneur visa in Ireland or the UAE.