The book that covers mutliple templates the best is
Savage Species; if you have that book, see the section on "Multiple Templates" on pages 142-144.
If you don't have it, here are the general rules: Templates can be applied in any order (whatever order makes the most sense for the creature's history, really), as long as at each step the creature remains of a legal type for the next template to be applied. The type of the resulting creature takes precedence in this order, from lowest precedence to highest:
Animal, Humanoid, or Vermin
Magical Beast or Monstrous Humanoid
Fey or Giant
Dragon or Humanoid (Shapechanger)
Aberration
Elemental, Ooze, or Plant
Construct, Outsider, or Undead
Templates of higher-precedence types override lower-precedence types, even if the lower-precedence types are applied afterward.
It is quite possible for a creature to have both the half-fiend and half-fey templates. According to
Savage Species, "When adding multiple templates, halves become quarters. A creature with both half-celestial and half-dragon templates becomes a quarter-celestial/quarter-dragon creature."
Regarding your specific questions, the following is just my take on things, but:
DeepShadow wrote:For example, if the Gentleman Caller "calls" on a shadow fey, is the result a shadow fey with the half-fiend template or an incubus/succubus with the half-fey template?
I'd definitely go with the former. Shadow fey with the half-fiend template. One could make an argument for the latter, but the former just strikes me as making more sense under the circumstances. (However, by the type precedence pyramid, either way the offspring would be of the Outsider type).
Since he's usually shapechanged when he...does what he does, does the child get any features from the form he's chosen?
Hm...interesting question, but I'd say probably not. At least, I'd say in general that's not the way it works. However, things don't always work in Ravenloft the way they "normally" do; the offspring could certainly get some features from his chosen form if the Dark Powers willed it.
Would it be possible to have a character who was a human with both templates this way?!
See above--it's quite possible for a character to have both templates. I'd say if the Gentleman Caller's half-fiend shadow fey child had a child of its own by a human, that child would be exactly that, a half-fey half-fiend human.