Yep, no clue about this, thank you so much for that info! I only knew that there is 1 CP-Violation phase which has not even been measured yet.
That's correct, although recent data excludes some possibilities for the value of this phase. So we know... at least a bit. Measuring the Majorana phases is much harder, as they play basically no role (their impact is very very suppressed). We need to rely on neutrinoless double-beta decays (decays in which two electrons and no missing energy are emitted) to get some insights.
I can edit the title if needed :p but care to elaborate on this a bit?
I couldn't find much about this, but I thought they were non-dimensionalized relative to a scale set by Einstein's gravitational constant.
I also read that 15 coupling constants to the higgs field? How would that work for the Higgs boson??
Masses are dimensionful quantities. They are given in giga-electronvolts (GeV) as mass and energy are equivalent in particle physics. Therefore, we cannot call them dimensionless quantities. They carry units.
As you proposed, we could trade the 15 masses for the associated 15 couplings to the Higgs boson (top-antitop-Higgs, bottom-antibottom-Higgs, etc.) and get something dimensionless. However, experimentally, we only know (in the sense of an experimental measurement) a few of those couplings (see the last figure in this post), so that masses are preferred.
Finally, for the electroweak sector, we need three inputs. The common choice is the fine structure constant (that is dimensionless), the Z-boson mass (dimensionful) and the Fermi constant (dimensionful). Other common possibilities all involve dimensionful quantities too.
Finally, for the Higgs sector we use the Higgs boson mass as a single input, which is again dimensionful.
To summarise, most of the free parameters of the Standard Model are actually dimensionful quantities ^^
PS: I am truly sorry for ruining this post ;)
RE: An Alphabet of the Universe? - The Dimensionless Constants