Is it permissible to take money resulting from participation in a global university open day for introducing academic majors, as a form of encouragement, as well as taking money for participating in market research surveys?

There is no blame on the questioner for accepting the money, and she is not required to ask the university about its source; for the basic principle is that what is in a person's possession is their property, and they may dispose of it through lawful means. Similarly, it is permissible to take money paid for holding oneself available for an hour or half an hour for the benefit of the organizing body conducting market research. This is permissible if a contract of exchange is made, stipulating knowledge of the wage and the time. If it is done on a basis of leniency and the gharar (uncertainty) involved is minor, then there is no objection to it.