Hello/Peace.
These are good questions.
I am a Muslim, so I will try my best to explain our views/answers to your questions.
Before I begin, I want to stress that God knows best about all that is in hear after, and we humans can only assume what might truly happen. With this in mind, here are my answers to your questions:
1) After Adam savs and Eve as commited sin and their sexual organs became visible to them, God Almighty was determined to punish them for their not following His commandment. The emphasis is not on their discovery of their sexual organs (perhaps the knowledge about sexuality itself) is not considered the source of the major sin here, but certainly it seems to be one of its consequences. God Almighty's reaction speaks for itself--there is no sex in Heaven. The Qur'an speaks of virgins as servants and usually, if you look closely at the verses in the Holy Qur'an their beauty is praised and they serve believers with heavenly food, or similar. There is also mention of young male servants, so, think of it as watress/waiter staff in Heaven. Don't know how better to associate it with (God forgive me!)
2 & 3) Women do not have to fight for attention for husbands, because there is no sexual relationships in Heaven
4) There won't be need for procreation because there will be plenty of humanity up there (our souls)
5) Heaven is described in many verses of the Holy Qur'an so please read a few if possible. But it is a place where the believers won't experience any pain, troubles, worries. Their souls will be clean and will have anything they might desire. They will rest in shades and the Heaven will have a beautiful smell. There will be angels greeting them, houris (the virgins) will serve them Heaven fruits/food, they will see waters flowing beneath them and palaces made for them.
In one place Qur'an mentions that the Earth will be inherited by the believers, and God states that He can create another Earth where only believers will enjoy it. Is this alluding to the Heaven on a renewed Earth? I don't know.