The standard first step is to make sure that the two scales are semantically equivalent. This is done by first translating the original scale into a second language. Then a completely independent bilingual person 'back translates' version 2 into the language of the original scale. Then a third person fluent in the original language compares the two scales to see if they are equivalent. You might be doing that already.

The second step is trickier and involves assessing cultural equivalence. I won't go into that here because there is no standard procedure yet.

Whether you allow respondents to choose their language or assign a language to each, you should record which language was used so that the effects can be studied statistically. If they are statistically equivalent, then their results can be combined for analysis.

And yes, if you measure covariates, their effect can be analysed.

Using translated scales in a multilingual context requires a combination of linguistic accuracy, cultural sensitivity, and methodological rigor to ensure validity and reliability across different language groups