Particle_Man said:
a) How would things be different if skin colour, hair colour, etc., were not tied to genetics at all? If a causasian looking parent and an asian looking parent could be the biological parents of an african looking child, for instance? I assume that this would eliminate racism (except between fantasy races, like orc vs. elf).
It wouldn't necessarily eliminate racism. If you assume that basic human qualities still carried over, there would simply be a different way to determine who was and who wasn't a part of the tribe. (Something like the Shibboleth test might work (in the book of Judges, one of the judges had a quarrel with one of Israel's tribes and, after defeating them, they held the river and asked everyone who attempted to cross to say "shibboleth" and, recognizing the accent of that tribe led them to pronounce it incorrectly, they killed anyone with the non-standard pronunciation). Remember that a lot of acts of genocide have and still occur between people who look relatively similar. The Hutus and Tutsis of southern Africa don't look different in anything near the dramatic way that africans and scandiavians look different. If any actual discernable qualities depended upon--or even appeared to be non-causally linked to--appearance, there could be something resembling racism there too. ("He has x-color skin, so he must be the smart one but shouldn't bother playing basketball" would be a conceivable reaction if x-colored people tended to do well in school but y-colored people did well in basketball regardless of whether or not they had the same parents).
However, there would possibly be other effects of removing genetics. If babies didn't look like their parents, it's quite possible that there would be less of a link between the child and the parent so abuse and infanticide might be more common. (It is certainly more common IRL when one parent is not related to the child than when both parents are). Come to think of it, in any fantasy culture, they should probably be more common than in modern America. I suspect that a lot of the modern western tendency to care for and protect babies at all costs comes from our Christian history. Certainly infanticide was quite common in pre-christian Greece and Rome, and if the sagas are taken to have historical content, it's quite significant that Sigurd's grandmother--who is presented as an admirable character--killed sent all her children except for one to her brother to be killed.
b) How would things be different if 10% of the population were openly gay, 80% were openly bisexual, and 10% were openly straight, and no one was in the closet or latent about anything?
To be blunt, this sounds to me like "let's imagine what the world would be like if it was all some giant music video/strip club." Gay, straight, and bisexual are quite recent social constructs that really only fit within the so-called sexually liberated culture of the post-sixties Western world. Various same sex attraction has been present in a lot of historical human cultures but never in the same form it is these days. For instance, it is generally argued (though Plato, Aristotle, and a lot of the ancient Greeks appear to have disapproved of this to some degree or other and the Spartans universally denied that there was any sexual contact between their Hoplites and boys as though such a thing would be shameful, so what is "generally argued" may contain a dash of modern propaganda) that it was common in ancient Greek culture for older men to have sex with younger men (who we would usually consider boys in modern culture). They were not, however gay or even necessarily bisexual in any kind of modern sense and the institution of marriage was considered a natural part of every man's expected life. (Women were, of course, as in most historically successful cultures, expected to remain faithful to their husbands so there was a decided double standard). So, you could certainly model a society with different sexual practices from ours but you'd do best to leave modern categories of sexual identity behind when you did so (note though, it might be more interesting and jarring to modern sensibilities to try making a game where everyone isn't a sex-crazed maniac out bonking everything that moves and a few things that don't. If you wanted a really sexually unusual culture, you might consider creating Plato's Republic in your campaign world. A society where sex is clearly for procreation rather than for pleasure would be a lot more unusual in D&D-land).
Another thing to note in that regard is that, a society where there is no particular bias towards procreation (since in your suggested society, there appears to be no particular preference towards heterosexual unions) or perhaps even a bias against procreation (since one can presume that a fair number of heterosexual unions are not meant to produce offspring), will not likely be a society that is reproducing itself in sufficient numbers to survive more than a few generations unchanged. (Modern western societies aren't anywhere near the percentages you describel, but quite a lot of them are reproducing at far below replacement rates). Unless this is a world-wide phenomenon encompassing all races, demographic pressure from the more fecund races (or other societies of the same whose practices and structures encourage reproduction at above replacement level).
On the whole, the things you're considering changing would--or ought to--have far-reaching implications for the history, social structure, institutions, practices, and cultures of your campaign world. If you tried to treat them as window dressing, it would make your campaign world a lot more shallow than someone who appears interested in creating a believable world (I notice you referenced Magical Medieval Society) would be satisfied with.