Hello Anon
#3 is the easiest – if you look back through this thread, you'll find plenty about the duchess's character, from various points of view.
As for #1, we have no information about the envoy's character. I suggest this approach: read through the poem, and mark the places where the duke addresses the envoy directly, e.g. line 5. In each instance, imagine the envoy's response. What does he do at line 5, for instance? Smiles, probably, and takes a seat, as directed.
When you've been through the poem in this way, you should have a collection of 'the envoy's probable responses'. From these, you can construct a portrait.
But it is difficult. It's a little like defining a shape by the hole it makes.
For #2, you'll find a poem written from the point of view of the envoy earlier in this thread. The poem is a letter from the envoy to his master. Why not use that as your basis? It's as good a guess as any.
Post your findings here, if you want some more help!
Good luck!
MrP