Batch supports both flavors inside a woff. It’s up to you to pick one, each of them has benefits and downsides. OTF will be close to the original while a TTF is mostly converted. A TTF flavored one can contain TTF hinting... Good luck

RoboFont will check the splines and convert them to two off curves splines in the next version. (in version 1.1 it doesn't check WOFF files, but it should :) Although WOFF files with PS outlines should work fine. Bonus answer: no ;)