A cemetery, burial ground, gravesite or graveyard is a place where the remains of dead people are buried or otherwise interred. The word cemetery (from Greek κοιμητήριον, "sleeping place") implies that the land is specifically designated as a burial ground and originally applied to the Roman catacombs. The term graveyard is often used interchangeably with cemetery, but a graveyard primarily refers to a burial ground within a churchyard.The intact or cremated remains of people may be interred in a grave, commonly referred to as burial, or in a tomb, an "above-ground grave" (resembling a sarcophagus), a mausoleum, columbarium, niche, or other edifice.
Yes it is allowed for a Muslim woman to visit the graveyard but with full Hijab as always.
Graveyard is a place for remembering the late persons, taking lessons of life and becoming more pious, not a place of celebrating birthday. Usually people don't celebrate weddings in a graveyard, not because it is Haraam to do so, but because it is not suitable. Same is the situation with celebrating birthday in a graveyard. It is not Haraam but not suitable.
If the deceased was not an enemy of Allah, you can pray to Allah to bestow His Mercy on those who are entitled. We also need to pray that when we die, we die with perfect faith and piousness.
No, we do not have such rule preventing pregnant woman from visiting graveyards.
Seyyid Ibn Tawus in Misbah Al-Zair says the best day to visit the dead is Thursday, but if you cannot do it on a Thursday, do it on any day you can.
Upon reaching a grave of believer, face qibla and place your hand on the grave. Then recite Surat Inna Anzalna (Al-Qadr) seven times, Al-Hamd. Al-Tawheed, Al-Falaq, An-Naas and Ayatul Kursi. When a person recites Suratul Qadr for a dead Momin seven times, Allah creates an angel to sit beside the dead person and protect the dead person from all afflictions until the day of judgement.
See Mafatihul Jinan in Adaab Ziyarat Quburul Muminin, Pg 655, Arabic Version.