Traditional subscription based journals require a copyright transfer agreement to be signed. Such agreements relate to supplementary files and thus include data. This means you would not be able to adapt, review or use the data unless publisher agreed.
Data should be made available separately. The data set should have its own DOI and thus can be cited appropriately. Ideally published under the creative commons licence CC-BY so that it can be shared, adapted and reused. However, this is not suitable for all research data and there may be instances where data has to be restricted or embargoed.
The related article or conference proceeding should be published as openly as possible. If it is open access, then if appropriate the data should be too.
Remember interviewees have legal rights over their recordings, even if not the copyright. You need to make sure that an informed consent form is signed, detailing what you are going to do with the data and how you are going to share it.
Such sources can in themselves be copyrighted. In such cases, you need clearance to use them. If such sources are in data centres, they will have advice on what to do.
Text and data mining (TDM)
TDM allows you to make copies of any copyrighted material for the purposes of ‘computational analysis’.
To do this the research must be non-commercial in nature and the researcher must already have lawful access to the material, for instance through a licence. Research contracted by an outside company is unlikely to be non-commercial. The copyright owners are unable to restrict access for the purposes of TDM and any contractual terms limiting TDM are unenforceable.
It is reasonable for publishers to apply measures to maintain their network security or stability but such measures should not prevent the ability to perform TDM.
If the results of your text and data mining are simply facts they are not in turn covered by copyright. Even in cases where the outputs contain original material, it may still be possible to share them using other copyright exceptions (fair dealing or the quotation exception). The law requires sufficient acknowledgement of copied works and this should extend to databases used for TDM.