1) It was recently discovered that the trainer job was not included in the list of jobs to be updated at the end of the day, thus it has no effect. This can easily be fixed by opening ".../files/scripts/Mansion.gd" with a decent text editor, finding the line starting with "var corejobs" at the top of the file, and adding to the list:
,'trainer'
2) The tamer specialization has not been changed to handle trainers working with trainees. Slaves working the same jobs will effect each other, but pairing different jobs has to be done explicitly. In "Mansion.gd", the line that starts with "if i.spec == 'tamer' &&"can be changed to:
if i.spec == 'tamer' && i.away.duration == 0 && i.obed > 60 && (i.work == person.work || i.work in ['rest','nurse','headgirl'] || (i.work == 'jailer' && person.sleep == 'jail') || (i.work == 'farmmanager' && person.work in ['cow','hen']) || (i.work == 'trainer' && person.work == 'trainee')):
3) The farm has job skill experience for each of the jobs: farm manager, farmhand, milking, bottling, milk merchant, and stud. How much impact the experience has varies considerably, and unfortunately farmhands never use that experience for anything.
4) The bottles use a copy-pasted function that was altered slightly for each; however the first line of text says piss for all of them. Generally(RNG dependent), if a person has a good fetish opinion for drinking that type of liquid then they lose a lot of stress, else they gain a bit of stress.
5) Fetishes have a small impact on the gameplay and I see no exceptions for the player, so I assume yes. I believe the save file is the only place to change the MC's fetishes at the moment; it's not too hard to do with a online JSON editor, but the daily updates can reduce the values you set unless you disable that option.
6) The code for creating people does not include a way to specify a hybrid race so it is currently not possible to intentionally generate them outside of breeding. There are no specific conditions against them being randomly generated but the chances are fairly low due to the various factors involved.