chandsingh

1) you can think of the risk premium as a spread, since, that is effectively what it is (in both equity and fixed income contexts).  And in reality, when things go haywire, the risk premium goes up, and that is often a bigger punch (but it’s also a bigger opportunity, since it may mean revert faster).
But since k = rfr + rp for small interest rates, then if rp is held constant, dk = d(rfr)
For answering the question “how do equity prices react, if rfr goes up,” it’s not necessarily a bad idea to hold the rp constant, though, more likely, you will want to assume that people panic in this situation and that rp goes up a bit too (and that would ideally be modeled explicitly).
2) a little algebra can help with this point:
(dp/dk) / p = (dp / p) / dk = (% change in price) / dk = equity duration