The Chicago Manual of Style:
6.60 In typeset matter, no more than one space should follow a colon. Further, in some setting — as in a source citation between a volume and page number with no intervening date or issue number, a biblical citation, or a ratio — no space should follow a colon.
The Chicago Manual of Style, sixteenth edition (2010) addresses this question somewhat obliquely, by limiting its style advice to what it refers to "two subtitles" within a title. After asserting (at 14.97) that "A colon, also italicized, is used to separate the main title from the subtitle," Chicago addresses the situation where a single title appears to have two subtitles:
14.98 Two subtitles. If, as occasionally happens, there are two subtitles in the original (an awkward contingency), a colon normally follows the first and a semicolon the second. The second also begins with a capital [as does the first].
Sereny, Gitta. Cries Unheard: Why Children Kill; The Story of Mary Bell. New York: Metropolitan Books / Henry Holt, 1999.
Although Chicago explicitly frames this advice as a way to handle such titles in a bibliography, there is nothing special about bibliographies that would forbid double colons there but not in regular text.
Chicago doesn't explain its dislike of double colons, but I suspect that the hostility arises involves the lack of clear hierarchical subordination that arises from a title rendered as X: Y: Z. Does the colon after Y indicate that Z is a subtitle of Y and a subsubtitle of X, or is Z on the same footing as Y as a subtitle of X? The colon/semicolon form, X: Y; X, indicates rather more clearly that Y and Z are on an equal footing as subtitles of X—just as in a list, where "the following: X; Y; Z" clearly marshals hierarchically equal-status entries X, Y, and Z. In contrast, "the following: X: Y: Z" is (by normal conventions of punctuation) fatally ambiguous with regard to hierarchical meaning.
Applying the Chicago style recommendation to your title, we get this:
Description of the eurotarget cohort: A european collaborative project on targeted therapy in renal cell cancer; Genetic and tumour related biomarkers for response and toxicity
With regard tog whether the G in Genetic should remain capped, Chicago advises simply that titles treated with sentence-style capitalization should begin "a subtitle" with an initial cap; it doesn't consider whether the subtitle in question is the only one, the first of two, or the second of two:
8.156 Principles and examples of sentence style capitalization. In sentence style capitalization only the first word in a title, the first word in a subtitle, and any proper names are capitalized. ...
From this, I infer that Chicago would approve of capping the G in Genetic in your example.
Best Answer
The Chicago Manual of Style, 14th Edition, section 5.97 agrees with you that a colon is used
It also notes, however, that
I personally would go for a semicolon in your 4th and 5th examples, and a full stop in the last, but the colon is certainly a viable choice.
(Section 5.99 also agrees with you that a colon is absolutely the correct punctuation to introduce an otherwise unadorned list as in your examples 1 and 2.)