Salaam brother very good question but your question has several questions rolled into one which I will try to answer inshallah.
1. According to Ibn Kathir's Story of the Prophet Book where he (ra) narrates the story of Nuh (as) the entire world was flooded since Allah (swt) submerged "all the land of the planet under water." Therefore from this understanding we take that all the people on Earth were drowned.
2. As for Nuh and Muhammad (saw) coming for all mankind. Here we need to understand that Nuh (as) was sent to his (as) people and at that time there weren't that many inhabitants of Earth nor was Earth as it is now in terms of the land and geography. Also when Allah (swt) says Muhammad (saw) has come for all of mankind He (swt) doesn't mean Muhammad (saw) as a person but him (saw) as a messenger ie Islam has come for all of mankind.
3. Christians use the bible to track back the creation of man to about 5,000 years BCE but we don't use the Qur'an in that way. So using the Christian model will naturally cause problems since we have scientific proof that humans have been around for far longer then 5,000 years BCE. The Copernicus Revolution was precisely on this point. Science came along and showed the flaw in Christian theology.
I hope this helps inshallah
### Originally answered as comment by Nozrul - Moved as answer by admin ####