A lady cannot use a comb on Shabbos.

Chapter 304 Section 1

In previous times, when a Jew bought a non-Jew for a slave, the slave is still a non-Jew. If he took upon himself the 7 mitzvohs of bnei Noach, he is biblically not allowed to do work for his master or any Jew on Shabbos. If he did not accept the 7 mitzvohs of bnei Noach, it is questionable if biblically he is not allowed to do work on Shabbos for his owner. For himself he surely can do melacha, even if he did accept upon himself the 7 mitzvohs.

After milah and tevilah though, he has all the laws of a Jew and cannot do melacha even for himself.

Chapter 304 Section 2

The owner of a slave who has not had a milah can tell him before Shabbos to go and work and make money for himself.