Mourning for someone whose parent is a mourner

Which mourning customs does one have to keep if one of his parents is sitting shiva (that is, one of his parents lost a close relative less than a week ago)? Please write a detailed reply.

The laws of mourning for someone whose parent or spouse is sitting shiva

1. This applies equally to the one whose parent is sitting shiva and to the one whose spouse is sitting shiva.
2. Until the deceased is buried, there are no laws of mourning that apply. 
3. After the burial, if the grandchild or the child-in-law is in the same city as the relative who is actually mourning and sitting shiva, it is customary that he keep those four laws:
   1. He should not take hot baths or showers. He is permitted, however, to wash or shower in cold or lukewarm water, as long as the water is not warm enough to be pleasurable. Someone who always takes a bath before Shabbat, is allowed to bathe before this Shabbos the same way that he always does.
   2. He’s not allowed to put on Shabbos clothes on a weekday.
   3. He’s not allowed to listen to music.
   4. He’s not allowed to take part in weddings, Sheva brachot and other celebratory meals. (However, he is allowed to participate in Bar Mitzva, Bris, or a completion of a tractate but not to eat there.) But if this joyful meal is held at his house, he’s allowed to eat there as well.
4. All these laws are only kept till the end of Shabbat. Afterwards, he’s allowed to do everything as usual.
5. This is the custom of the Ashkenazim. Most Sephardic communities do not have this custom.

(Note: these are the relatives after whose passing one is obligated to sit shiva: father, mother, brother, sister, son, daughter, spouse.)

Shulchan Oruch, section Yore Dea, chapter 194, §3