May one brush his/her hair on Shabbos?
Using a brush: It is forbidden to brush [hair] with a brush on Shabbos, even with those [brushes] made of swine hair.
The reason for this is because: it is impossible to avoid removing hairs in the process.
Using ones hands: However it is permitted to separate the hairs apart with ones hands.
One may not use a brush to brush one’s hair on Shabbos as it causes hair to come out. However one may use ones fingers.
May one use a soft brush to brush their hair on Shabbos?
To straighten out the hair: One may use a soft brush to gently brush hair on Shabbos. One may not brush with force is this can lead to pulling out any hair. As well it is proper that the brush be designated for use only on Shabbos.
To make a design: See above!
May one brush their Sheitel on Shabbos?
If the Sheitel is wearable without the brushing: One may brush a Sheitel using a soft brush and doing so softly in order to avoid pulling out any hair. As well it is proper that the brush be designated for only Shabbos use.
If the Sheitel is not wearable without the brushing: Then it is forbidden to be brushed even in the above method due to the Fixing prohibition.
 Michaber ibid
 Rama ibid
 Kitzur Shulchan Aruch 80/31
 Ketzos Hashulchan 143 footnote 6; Piskeiy Teshuvos 303/10
 The Minchas Shabbos [80/117] concludes that it is forbidden to do so, although he brings that there are those which are lenient and a Baal Nefesh is to only do so in the way described above.