hi, thank you for the great questions and glad you are enjoying the thread :-) I did want to focus on the internal aspects as only certain (misunderstood/inaccurate) external rituals of Islam are ever discussed in mass media.
in terms of deceased Muslims. not only is cremation not permitted, but any kind of mutilation of the body. we are also told to handle body with extreme gentleness and respect. this is because the body is sanctified and needs to laid to rest as it has its own journey. the spiritual process of death lasts beyond the immediate moment of the souls departure.
the handling of deceased humans applies to non Muslims as well. we are also to handle them with great respect. for example mutilation of dead bodies was common historically but Muslims were forbidden to do this by the Prophet SAWS. this happened after a battle where a lot of deceased Muslims were mutilated (including the uncle of the Prophet SAWS whose heart was eaten by one of the opposing leaders who later became Muslim and was forgiven). the Muslim soldiers wanted to avenge the mutilation but were forbidden by the Prophet SAWS.
the physical process of burial is undertaken by men... just for practical purposes I guess? and I guess these days it's mostly automated. women can be present at the burial... they just stand back i think more of a matter of allowing the space for what needs to be done. i have attended burials without any issues. women attend funeral prayer and all the other funeral rites. bathing of the deceased is done by members of the same sex.
so one thing to be made clear is that a woman on her period is NOT considered dirty. in fact while she is on her period, all her namaz are counted as if she has read them and she gets reward for this. she can only not pray the namaz or fast (it is stated in the Qur'an and also applies for 40 days after birth). she can pray otherwise without any issues with slight adjustments and she can still go to the mosque. I personally do meditation (on the word God), read prayers and listen to Qur'an recitation to bring me that peace during those times. I think definitely culture affects how these rules are interpreted and communicated. and often its not pleasant. but the point of these rules is not to exclude women but grant them relief from obligation.
the concept of 'ritual purity' in Islam is quite complex. men are subject to similar rules but these work differently because of differences of physiology. if you want more details, I can provide this. :-)
yes, it's quite an interesting thing to do as there are a lot of similarities in the message. and also the Qur'an describes the history of the Abrahamic religions including Christianity in a lot of detail.
In terms of researching Islam, for me there were two parts, theoretical and practical. A biography of the Prophet SAWS is a good start. Muhammad by Martin Lings is good, although it has a few(quite significant) inaccuracies. it provides a broad overview. Translations of the Qur'an are best read while in discussion with a Muslim scholar or someone who has reasonable knowledge of the Qur'an as it is incredibly complex. Books by Imam al Ghazali RA helped me a lot. Ihya Ulum al Din is a huge text, but helpfully broken into subsections so one can select according to areas of interest. Imam Al Ghazali RA's Alchemy of happiness and The Book of Assistance by Imam Ibn Alawi al Haddad RA are a great start to examining the 'inner aspects' if Islam. The Cambridge Muslim College has some great free resources and Shaykh Abdul Hakim Murad has a great deal of content on YouTube which I have found helpful and enjoyable. I really wish there was a good book about the scientific miracles of the Qur'an, but unfortunately none that I would recommend.
in terms of the practical part, I felt experiencing the lived aspects of the religion definitely helped me understand it better. I started with praying once a day and some other very basic things... and it helped make sense of what I was reading.
sorry for the extremely long ranty reply!