As far as my testing has done, the only way to have a pure child is to have the blessing of a similar member of that race, easiest way to do so would be to train another member of that race, remove whatever blessing you currently have by looking in your blessing menu (I don't recall how early you unlock the blessing options but it should be early enough), and then doing a quick training session with them (do not have to have sex/complete it, think you do have to maybe touch them though and they do have to be tamed).
In terms of what does/doesn't transfer, I can assure you right now that rare skins don't seem to transfer (i.e. if you somehow have two albinos and get the blessing from one/impregnate the other and also vice versa, it's unlikely you'll get albinos from either), BUT I do think simpler traits may pass on. If you're going for the clear value of hairless then this doesn't help, but any race with a vaginal cover (naga, a lot of the insects, etc) you can eventually purchase a surgery type thing that removes the cover which makes it appear as if they are hairless, and there's also the razor in the tools part of the shop (which is good even on hairless slaves as it also helps raise shame I think). Sorry can't be more help on what does/doesn't, as much as I've enjoyed playing the game I usually just search for cuties in the shop and play "stock market" where I buy slaves when they're cheap, let them sit in the cells untouched while I work with the current focus, and then check how they sell every day and if it's over a 3.0 or so I tend to sell.
Oh, one final tip that may/may not be super important: if you look in the Slave Matrix folders, you should see a file named "Config". Right-click it and choose to open with Notepad and you should see two lines of text. I think the "Read Me" file explains it more so I forget what "Auto Sort" does, but "Simple Mating" in the file will have either a 0 or a 1. A 0 means that previous generations count if you try to do mating (i.e. when you look at a slave, look who their parents are, their traits may pop up in a child if Simple Mating is 0), but a setting on 1 only counts the slave/blessing used. As noted before, I've tried to just get an albino and that's the method I used, but assuming stuff like hairless/muscled can be passed down, that may make it easier to do so.
*auto sort will sort by races based on when they're added, so if you buy a harpy first, then naga, then another harpy, default is Harpy-Naga-Harpy, but afterwards it'd be Harpy-Harpy-Naga if you change auto sort from 0 to 1. Also also, 'mixed' children that combine the blessings of different races, have different values. I haven't fully dived into it, but say, a harpy/naga combo would have a lower base value than a phoenix/ouroboros combo I'd imagine
