As has been said above, the rig is clearly a Ketch rig. In English, the names of headsails vary with, country, region and time, but using the terminology that I grew up with in the mid-20th century in a U.S. mid-Atlantic state, I would call the sails from left to right as follows:
Flying jib (sometimes also called a Jib Topsail), Headstaysail (pronounced 'hed sta' sil'), Forestaysail (sometimes simply called the jib, lately shortened to simply the Staysail), Mainsail, Main topsail, Mizzen, and Mizzen topsail.
While the lowers are gaff rigged, that would not be included in the name of the sail. (In other words the order would be to given as 'bring in the main sail' and not the 'bring in the main gaffsail'.
Just out of curiousity, what is the purpose of your research?
This is the rig that I have on my ship, with the exception that my topsails are triangular, not square. The main purpose is that I am considering translating my home-site into an English version. The home-site started as a story about the ship that I wanted to tell my grandchildren. But it has somehow grown alive and lives its own life outside my control. It contained parts of the history of Norwegian ships from the Vikings till now. The story of this ship as an original fishing-ship. Then parts and bits of seamanship, explanations of words and concepts of navigation, traditions of shipbuilding, maintenance of wooden ships etc. It really has grown into a monster.
Then I discovered that I had never heard any English names for these sails. Even in a correspondence with the ARC administration when I considering part-taking in the ARC race, could ARC give any other names than just jibs. So if I am to translate the home-site, then of course the names of the sails must be translated as well.
The second purpose is that I plan to sail from Norway to the Caribbeans this summer. It just may be that I will need to take some English speaking crew with me. In that case I do not want to have any misunderstanding concerning the names of the sails in the case where something must be done with them.
As an example, hull-speed is reached at 35 knots (approx. 7,5 knots). If the wind gets stronger it will be time to reduce sail-area, depending of the wind and course, the choice of which sails that is to be saved will differ.