Transformation is affected both by luck scales, and personal luck of the caster. There are two Luck-granting trinkets that can be fairly easily acquired, and they both seem to stack in decreasing the chances of a bad transformation.
This is literally the first time I've ever heard of personal luck affecting anything out of combat. Do you have a reference for this, or is it just personal experience? (I'll test it myself at some point either way, but now I'm rather curious.)
Also no, I don't think bad transformations reduce magic paths. I never saw it happen at least, besides the transformations to feebleminded or mindless forms that just take away all paths.
It's only the Feeblemindedness that's eliminating spellcasting. Mindless beings can still cast spells; e.g. Golems, Onyx Oracles, Colossal Fetishes, and the whole sidenote about Mindless casters not being affected by or able to cast Magic Duel.
As someone who's spent a lot of time on the mod inspector, a lot of animal forms have path penalties (and a few have bonuses IIRC).
A lot of the units that are Transformation targets have #fooattuned, which is a Transformation/Gift of Reason-specific command to add a level of a given path upon transforming/becoming a commander. However, none of them actually have positive or negative path boosts.