KMadCandy
giggling permanoob
In war situations it isn't that bad. Sometimes it is, though, in particular in cancel deal situations. I often have a situation where the master hates me and won't trade much but the vassal has some good trading relations. If they're both the same civ, I can never know who I'm asked to cancel deals with. Probably the most annoying of these situations.
actually you can. you can check the foreign advisor during a demand, but i didn't know that at first since i can't access it my usual way (F4). i had thought it was by design. i have to click the mouse on the button in the corner of the screen. then i can go check how whoever's making the demand feels about the various so-and-so's and usually can tell which ones he thinks are vile.
the trade screen is still up in the background while you're checking the advisor. i do this for tech demands too, to check whether it's a monopoly or maybe it's so well known that it's worth giving in, or to check the powergraph to see how scary the guy is.
what i've heard is that if you leave the advisor screens by hitting "escape", rather than clicking on exit with your mouse, that closes the diplomatic trade screen too with an automatic "no" answer. i haven't tested that since i'm little miss ultra-cautious, but be careful.