In this exercise, the key signature has two flats but it's marked as C minor. There's a footnote that simply says 'modal key signature'. How do I work out which mode to use in my harmonisation?
You don't need to know which mode you need to use in order to complete this exercise. You simply follow the chord symbols on the bottom.
I would hazard a guess that "ic" means the "cadential" version of the i chord and would therefore be i 6/4, but consult what the book says "ic" is before committing your answer.
Following the chord symbols on the bottom strictly will eventually lead to you using a B natural (in the V chord) and an E natural (in the I chord). At this point, fuhgheddaboudit mode-wise--no mode of any major scale contains Eb, E, and F.