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.

Is it permissible for a guardian (Big brother) to unlawfully stop his sister from getting married?

If the guardian denies her right in getting married for an unlawful reason, she should go to court in order to settle that matter, and the guardian is considered sinful in this case.

I wear braces because I had an accident. However, Iam afraid that I could die and be buried while wearing them because they are permanent installation. Is this forbidden? I also wear false teeth. Should I ask my children to pull them out after I die?

What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?

Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.