Were (or are) the measurments that showed the inconsistencies (to SM predictions) of Rc and Rb considered non-serious? In fact reading in a paper "taking those measurements seriously" made me giggle and think if I should take what's written "seriously" (or if I am badly mistaken).
Q2:
And finally I don't really understand the mass-hierarchy for the fermion mass spectrum (again mentioned in the intro).

The top quark mass is relatively as larger to charm quark mass (3rd to 2nd), as charm is to up (2nd to 1st)... In numbers:
[itex] \frac{m_t}{m_c} \approx 134 ~~,~~ \frac{m_c}{m_u} \approx 561 [/itex]
Any idea? Or is the "relative" mass compared to something else (like the QCD scale)?

See the introduction of the first paper for references and significances. 3.5 and 2.5 sigma, respectively - something that can be a statistical fluctuation, but it could also be a hint of something new. The paper is discussing effects that can influence the value, but you can say "I don't take that 'seriously', it is probably just a statistical fluctuation".

The quark masses have a huge ratio for the third generation if you compare everything to the first generation, e.g. charm/up ~ 550, while top/up ~ 75000.