See Orach Chaim 260:1/mogen avrohom/taz/mishne brura
Cut nails on Friday because they regrow on 3rd day, so if you do it Thurs it will be on shabbos and that would not be kovodik to have the nails grow on the day you bedavka want them cut for.
From Rashi mashma that people used to cut on Thurs but probably because they didn’t have time on Friday.
Not to cut on same day fingernails and toenails so do latter on Thurs and former on Fri.
Don’t leave nails lying around because danger to pregnant woman. Gemara says chasid burns them, tzadik buries them, rasha throws them wherever. Ri Milunel says it’s a problem because it will frighten the woman (she will think she stepped on a scorpion) but this doesn’t square with the understanding that if there’s shinui mokom there’s no sakono. Machlokes whether just moving them around in the same room is considered shinui mokom (as one eitzah is to just sweep the floor).
Specific order of fingernail cutting given, Maharam and Ari not concerned, tov lizaheir lechatchila.
Some places follow tzvoa’s R. Yehuda Hachosid to not haircut/shave/nailcut on rosh chodesh even if it falls on erev shabbos.