1. How can I confirm whether someone was captured at the battle of Dunbar?

Answer: the only surviving list of those captured at Dunbar (officers only) is among the Lothian muniments at the National Archives of Scotland (reference: GD40/2/16). This contains the names of officers only (see Image 1 for an extract from this). You can see an image of the original document and an alphabetical index of names on the list by clicking on the Virtual Vault in Research Tools. For published information about Scottish prisoners deported by Cromwell see Massachusetts Historical Society Proceedings, vol. 16 (1928), pp.4-29; also David Dobson, Directory of Scots Banished to the American Plantations 1650-1775 (Baltimore, 1983).