Hi,
I won't be able to answer all your questions, but I will answer those I am confident with.
1a. Why are visual depictions of Muhammed and Allah forbidden in Islam?
1c. Are there religious figures in Islam that can be visually depicted?
In Islam it is forbidden to draw
anything that has a soul, be it human or animal. Statues of living creatures are also forbidden.
It is especially forbidden to draw the Prophet Muhammad (May the peace and blessings of Allah be upon him) because it can lead to people worshipping the images of Muhammad, rather than worshipping God.
By the same token, it is also forbidden to draw other Islamic religious figures, since it can lead to an exaggeration of their status that can ultimately lead to worshipping of the images rather than God.
7a. What is Islam's position on the role of women in society?
One of the important roles for women in Islamic is to take care of their household and children and raise them properly and according to Islamic standards. This is obligatory (if they have a family). It is also obligatory on them to gain knowledge, and there should be a balance between religious knowledge and non-religious knoweldge.
Women are also expected to assist in the betterment of society in general and of the Muslims. This does not mean they
must work, since they can fulfil this duty, for example, by raising their kids well, so that their kids are a benefit to society rather than a menace, or by doing charity work etc. But women are of course permitted to work, however they should insure that working does not mean they are sacrificing the well being of their families.
That is a very brief answer... if you want to know something more specific please ask.
7b. Why are Muslim women veiled? Is this a strict rule? Are there denominations that consider it unnecessary?
Muslim women cover primarily because God told us. The reason He told us to do so is for us to remain modest- it is seen as immodest for women to show their bodies, and to protect us from the lustful gaze of men and their approaches (flirting/inappropriate behaviour etc). It also makes for a better society where people aren't exposed to semi-naked bodies where ever they go, and so there is less temptation.
It is not, as some people love to claim, a way of keeping women in the background or oppressing them. Rather it is a way of honouring women. They are respected for who they are as people, and treated accordingly, and not for their beauty or body.
God said in the Quran:
O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies. That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allâh is Ever Oft*Forgiving, Most Merciful.
(Chapter 33: verse 59)
30. Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc.). That is purer for them. Verily, Allâh is All-Aware of what they do.
31. And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc.) and not to show off their adornment except only that which is apparent...
(Chapter 24)
It is a strict rule, and there is total agreement amongst the scholars of Islam that it is obligatory for women to cover everything except their hands and face (some add feet) once they reach the age of puberty.
There is disagreement amongst scholars about whether covering the face and hands is obligatory or not. Some say it is obligatory, others say it is not.
Hope that helps!:)