Yes, it is generally mandatory to obtain ethics approval for a survey on the cross-cultural adaptation of a questionnaire. The reason for this is that the survey involves human participants and has the potential to affect their well-being and privacy. Ethics approval is a process of review and oversight by an institutional or national ethics committee to ensure that research involving human participants is conducted ethically and responsibly.
Cross-cultural adaptation of a questionnaire involves translating and validating a questionnaire to be used in a different cultural context. This process may involve making modifications to the original questionnaire and may require additional steps to ensure that the adapted questionnaire is culturally appropriate and valid in the target population. It is important to obtain ethics approval to ensure that the rights and welfare of participants are protected throughout the research process.
In addition, obtaining ethics approval may be a requirement for publication of research results in many academic journals. Therefore, it is important to consult with the relevant institutional or national ethics committee to determine the specific requirements for ethics approval for your research.
The answer is always, Check with the Institutional Review Board at your university.
It's possible that your kind of research is "exempt" from this review, but that they would want it submitted to review to determine that it is "exempt".
It also may depend what the purpose is. For example, in my university there is a distinction between survey results that will published and those that won't. For example, you can survey an undergraduate class about their assessment of the course, but if it isn't being used as publishable research, it doesn't need institutional board review.
I agree with Dr Sal Mangiafico that it depends on your organisation and generally would also say yes, almost everything is necessary for ethics approval.
I say this from being a member of my organisation's ethics committee and I always have to recognise particularly that people from different cultures need to be monitored most carefully.