Servant: The rain has stopped, Your Majesty. We can now continue with the portrait.
King: So I should hope, (Is this the same as I hope so?) Albert. First time we've
had the whole family here for six years.
Photographer: Let's try and get one in. Take a picture?
We'll need both banks (What are these banks?) to fill light.
Assistant: I've already strung the cables, (connected them?) sir.
All yes.

Stringing and connecting are not exactly the same. Did you ever string lights on a Christmas tree? "Stringing cables" is running them from point A to point B to point C. Connecting them comes afterward.

I assume "banks" here refers to "banks of flood lights or spot lights." - a cluster, or wall of lights.
Thanks for your help, Avangi!