We live in Australia and I would be grateful if you could answer the following questions in relation to Australia.
Are women who are in their period allowed in the mosque? The visit may be to see the mosque by non Muslims or to learn Islam by a Muslim.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is forbidden for a menstruating woman to enter a mosque for the generality of the Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said: "I do not make the mosque lawful, for a menstruating woman nor for an impure person (from sexual impurities). And also for his command to Aisha when she started menstruating in Hajj: "Do all the rites of Hajj just as a normal person does except the Tawaf (circumambulation) round Ka'ba until you become pure."

A Muslimah has to keep away from mixing with men particularly if they are non-Muslims on the other hand she should encourage her male relatives to do Dawah. There are many ways to gain Islamic knowledge or increase it, for instance by Islamic cassettes, books, etc.

Allah knows best.