Charles and I discussed this and we have a few points to make on how easy/hard this is.
1) In general doing a miracle in someone else's chancel
will be seen as at best Highly Improper and at worst a
Grave Threat.
2) If one cannot actually see into the Chancel, or does
not know what is there, it can be quite difficult to
perform said miracle effectively (but it will still be
seen as Improper and a Threat), e.g. doing a creation
of a small clockwork critter might succeed, but inside
of a Large Rock.
3) Any alarms will of course go off
4) Usually there are easier ways to "knock"
5) Any chancel worth its name will have _at least_
regions which are warded (and sometimes of course the
whole chancel) against miraculous activity from
"outsiders".
Q: Does the etiquette with Miracles in Chancels extend to the Gate area?
Divination is not obvious and hence unlikely to cause offense. They might be annoyed if you go around changing the geography around their front door, but, since most Nobles can't tell where Chancel gates are located, it is difficult to take offense of a casual act in such an area.
Q: Re: #1 above: Does this include all miracles done within or into a chancel? It seems extreme to deny Nobles any Divinations while they are guests in a foreign chancel. Wouldn't it render them (Anchorless guests) blind to the outside world and their own business there?
A: I think we overstated intially. What we meant was, it is Highly Improper to miraculously affect someone else's Chancel without permission. Likewise performing any miraculous action that affects (or enters) someone's chancel without so much as an introduction would be to completely deny the soverignty of the Chancel's rulers - an insult and a threat at once. If permission is granted ("I can turn that tree into a dancer for your chancel if you would like.", "Sure.") then obviously this is ok. Likewise, performing miracles from inside someone's chancel that affect the outside world has no greater chance of offending the chancel's inhabitants than it normally would.
Just behave like nobility visiting another nobility's home and fortress and you won't go far wrong.
Ghost miracles are less of an issue - sending one in would just be an insult. (Also, remember that Ghost miracles are not affected by Auctoritas or Defender's Blessing since they have no substance.)
Q: Are there general rules of hospitality for Nobles?
If you mean by that, "are there rules whereby a Chancel would be forced to allow you to enter" (such as rules of hospitality in many ancient peoples such as the Norse and Arabian), no. Most Nobles, however, make a strong effort to treat fellow Nobles with the respect due to their station. (And the higher one's Realm, the greater one's aura of Nobility, the more respect one is likely to receive initially.) It may be a cold respect, but unless someone is being intentionally hostile, they should, at least, be willing to listen to what you have to say, especially if you show up in person (as opposed to sending emisaries).
Q: Is using an Aspect miracle on another Noble detectable, if it's not an immediately obvious one?
A: Depends. If the Noble's Auctoritas would oppose it, then yes. A Noble knows any time their Auctoritas acts up. On the other hand, if one wished to be inhumanly perceptive, there is no reason anyone else would notice. Even for things like moving very quickly, if the Noble isn't looking and as long as the movement didn't enter their Auctoritas, they would not necessarily notice. (Of course, if their natural aspect were high enough, the might notice the movement by dint of their own enhanced perceptions, but not due to some innate ability to detect miracles.)
Q: What are the rules of politeness in terms of what we can ask for [in terms of refreshements]? In other words, is it perfectly acceptable to ask for, say, a single plum floating in a man's hat, or pixie tears, or whatever, or would anything other than tea be looked upon as odd and rude?
A: Anything obviously offensive (e.g. "the head of Kep on a silver platter") of course would be rude. If you ask for something odd such as pixie tears, they may or may not have it.
Of course, flowers might be construed in a ...negative... fashion, if they happen to be certain ones, as you might imagine.
If you have something specific you want to ask about feel free, I think the two examples you give below would be non-offensive (though they may confuse or surprise your host ;)