2 To prove extremities of bloody fight,

prove extremities > experience [the] extremities (i.e. they are determined to fight to the death)

3 At her speech their rages gan relent,

gan > did; began to

4 And calm the sea of their tempestuous spite: 5 Such power have pleasing words; such is the might 6 Of courteous clemency in gentle heart.

gentle > noble

7 Now after all was ceased, the Faery knight 8 Besought that damsel suffer him depart,

suffer him depart > to allow him to depart; to grant him departure

9 And yield him ready passage to that other part.

ready > prompt; direct that other part > [the mainland]