What are the differences between female Modern Orthodox/Modern Orthodox Liberal Jews and Conservatives in terms of women's modesty? My question applies both to dress and social interaction - shaking hands with men, singing or performing in public (not at the shul), wearing pants outside of the shul, married women covering their hair, mixing in public places such as work or swimming pools, etc. I would like to know the 'official' stance of the various groups and how it is in practice.
I couldn't find any relevant teshuvot on the Rabbinical Assembly web site, and as already noted by Seth J, there isn't a single authority for Orthodox (Modern or otherwise). I can describe what I have observed (primarily in one city). I often attend a Conservative shul for weekday services and occasionally others, and I've visited several Orthodox congregations a few times.
Women in Conservative synagogues may wear skirts, dresses, or pants. Sleeves may be short or long, but necklines are moderate to high. Covering hair appears to be uncommon. Women and men shake hands and there is mixed seating at kiddushes. Social activities do not appear to be gender-segregated. Some women work outside the home and do not limit themselves to gender-segregated jobs. I don't know what happens at public swimming pools.
It's harder to tell which synagogues are "Modern Orthodox" versus some other Orthodox designation. I've been to Orthodox synagogues where men freely shook women's hands and where women wore short sleeves (not pants, though). I've been to others where these things don't happen. This is somewhat confusing. A woman who told me she is Modern Orthodox dresses the way I described Conservative above (but no pants in shul), and she has both male and female coworkers.
There are vast differences just among the modern Orthodox. If you want "official", you'd have to define some authority to whom everyone subscribes, which is impossible.
The United Synagogue of Conservative Judaism issues rulings that are supposed to be binding, but aren't, on all member synagogues. Much less are they followed by individuals.
Orthodox Judaism doesn't have any such centrality, save in a few places in which the government has sanctioned an official chief rabbinate, like the UK or Israel, for example.
Orthodoxy, however, by definition, lends itself to following authority, but it's a question of whose.
Many modern Orthodox Jews follow the same standards as more "ultra-orthodox" Jews on virtually all matters of Halachah, and merely engage more in modern life, so that their standards of modesty are totally within the parameters set down in writing in previous generations. Others, though, see modesty as subjective to the standards of society at large, and therefore, while still adhering to a standard (which may be hard for other groups to identify), is much more in line with what one might see elsewhere in society.