I wish to Pray at the Mosque, but I couldn't because I am a Woman. How can I get such a Reward?

All perfect praise be to Allah The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions                                                                                                                                                                                                                            Abdullah Ibn Masood (May Allah be Pleased with him) reported that the Prophet (PBUH) said: "Her prayer inside her home is better than its courtyard, and her prayer in her own bedroom is better than inside her home." [Abu Dawood]. Her staying at home, and not going to the mosque in obedience to Allah`s injunctions entails a great reward similar to that bestowed on a man for going to the mosque since the Mercy and Blessings of Allah Prevails. And Allah Knows Best.

When Iddah is Initiated for Deceased's Wife?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Iddah is observed on the same date at which her husband passed away for four months, but as for the pregnant, it is observed at the date she gives birth. And Allah Knows Best. 

Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?

It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.

Is it a condition that one should offer two sacrifices for a male newborn?

It is desirable to offer two sheep for a male newborn, and one for a female newborn. Offering one sheep for the male newborn is also permissible as it observes the Prophet`s Sunnah in this regard.