Cole is an interesting case... this is one spirit who seems to have forgotten its true nature, instead stealing another identity - and it only kills those who can actually see it, seemingly placing great emphasis on eye-contact as he does so. It could be that Gaider was exploring an emotional phenomenon here; the intimacy of death. As Cole said, in the moment of the killing, he became the single-most important thing in the world for its victim, which may have been the anchor it needed. This might explain why it simply vanishes as soon as Lambert reveals the truth, returning to the Fade as said anchor is cut at its source.
On the other hand, this could just be the spirit not understanding its own nature, and it is as you say the blood that provides the necessary energy to power a semi-permanent rift through the Veil. This in turn might explain how Cole manages to return later, seemingly at will... In short, your theory makes sense, too.
Blood is more powerful than lyrium, but depending on how strong (or weak) the Veil is, ordinary magic can be perfectly enough to bring a demon into the mortal world, just like it suffices to bring a mortal soul into the Fade. Places with strong magical activity tend to have a weaker Veil, and you already mentioned how some demons manage to break through on their own down there.
As far as the summoning goes, I think we've got enough material to at least make educated guesses by now. The setting does know certain means to "trap" demons (like the circle keeping the possessed Pharamond in check), though most of the time demons seem to be summoned because the summoner wants them to fight for them or they are not aware of any potential safeguards or they consider them unnecessary. Either way, a demon still needs to be brought through the Veil - they often try this on their own, but during a summoning process you've got one or more mages "from the other side" actively helping the demon by using their magic to tear a hole into the Veil, allowing the demon to slip through and retain a presence without getting "sucked back" right away. Magic to the Veil is very much like CFC to the ozone layer; I guess that whilst all spells have a certain weakening effect there are some specifically intended to tear a hole through the Veil, bringing the Fade and realspace closer together to allow crossing over.
At least this is how I'm interpreting the available reading.
And yeah, I love threads such as these. Nice exchange!