In The Amber Spyglass, Will and Lyra (& Chevalier Tialys and Lady Salmakia) must leave their Daemons behind when they cross the river into the world of the dead. If Humans in His Dark Materials are made of three parts (body/soul/daemon), why don't Lyra and Will experience large personality changes while they are separated from their Daemons? In particular, there is a scene where a flicker of Romantic understanding passes between Lyra and Will. Why should this be possible in the absence of their Daemons? People might answer that in fact there are changes that I didn't notice, or give an (in universe[s!]) explanation for why they would seem the same.
Yes, normally it is not possible to separate body from daemon, but these were not normal circumstances. They were in the Land Of The Dead, which seems to be all the difference. Please notice that it was neither easy nor without side effects.
There are instances where separation (long-term or long-distance) from daemon is possible: witches and shamans, among others. IIRC both involve very specific place and ritual to succeed.
The bodyguards you mention were intercised, which is severing connection to the daemon, not separating from them for any given period/distance and even then it wasn't 100% successful. Some do not survive this process anyway.
As for the second question - they were separated from their daemons, but not permanently. The connection is still there. Nothing really prevents them from acting normally. Absence is not inexistence.