Do I need to frame the fine art paper prints?

Yes.  You will need to frame the fine art paper prints, under glass, preferably with a sealed up back, to act as a dust cover and a barrier for moisture and insects.

You say that the canvas prints, mounted to foam board, require framing.  Does that have to be under glass?

No.  The canvas prints do not need to be framed under glass.  A sealed up back is optional.