The first problem was caused by too long headings, while the second by mathematics inside the pdf bookmarks when using hyperref .
The solution I found by googling around is what I also wrote in this Tex StackExchange answer:
\chapter[\texorpdfstring{TOC title \( inline math A \)
}{TOC in pdf bookmarks}
]{\chaptermark{header} Chapter title \( inline math A \)}
\chaptermark{header}
\label{CH:Chap}
In this solution the pdf bookmarks are defined by \texorpdfstring{#1}{#2}, where #1 is the title inside the pdf document while #2 is the pdf bookmark.
The [shorter] heading is defined by \chaptermark{header}. The repeated command is not a typo, but it is needed in order to have the right behaviour in every situation (do not ask why since I do not have any idea, just by tentative; if you know the reason, please comment below. EDIT (2016-03-22): Some explanations can be found HERE)
Important: the solution also works with \section, just change \chaptermark with \sectionmark.
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