Please try to give examples that compile. I removed extraneous dots,
replaced '\include{chapter|app1#}' with \chapter{#} & placed a dummy
bibliography in the example you gave.
In case 1, my TOC had the bibliography as a section in the last
chapter, before the appendices. This is correct behavior for the
strange place you placed the addcontentsline.
In case 2, I had the same results you did & this is expected.
> %\addcontentsline{toc}{section}{Bibliography} %2
>
> This seems better, but the entry looks as if Bibliography is part of
> appendix B.
This is correct behavior for your input--the ToC line called for a
'section' entry, rather than a 'chapter' entry.
> And indeed, again the title of appendix B shows up on top of the
> page, i.e. the bibliography is still recognised as part of the appendix.
I don't know what packages you are using, but this might be the
correct behavior if none of them create chapter headings for the
bibliography. You can explicitly place the bib in a new chapter (or
chapter*).
Depending on the packages that you use, you might also need to use one
or both of these lines:
\cleardoublepage
\phantomsection
See <
http://www.tex.ac.uk/cgi-bin/texfaq2html?label=tocbibind>
--Rick