How do the Vikings not become Christian?
Even as the Vikings were militarily successful, they were falling under the cultural sway of the geo-politically weak Christian nations. Clearly, there was something powerfully attractive about Christianity.
In order for your Vikings to stay noticeably Viking, and not generically Northern European, they have to keep their own religion, possibly developing it into something that can compete with the proselytizing success of Christianity and Islam.
Why does this Viking/Muslim Europe advance so fast?
This is a tricky one, since it is not entirely clear what made Early Modern Europe develop so fast. It is undeniable that a region that was probably the least developed of the four major cvilization centers of the Old World (out of China, India, the Middle East, and Europe) in 1400 ended up clearly ahead as soon as 1600 and far ahead by 1800. But what caused this is up for debate. Suggestions include:
- The competition between secular and religious authority and the legacy of feudalism lead to stronger property rights in Europe than elsewhere.
- The legacy of Republican Rome and the tension between independent secular and religious authorities undermined the absolute nature of monarchy. For example, only Europe had a situation where a powerful King (of France or Spain) nominally owed religious obedience to a religious leader outside his own authority.
- A large number of relatively stable states limited tyrannical governments' ability to stifling trade and development.
- A large number of states lead to increased competition and warfare, and fast development of weapons technologies.
None of these reasons seeems fully satisfactory, so a combination of them is probably more accurate.
In any case, if your Viking-Muslim continent gets together, how do you reasonably replicate the fast growth and technological development (both in shipbuilding and weapons) that allowed Europeans to go to other continents and push the natives around?
What drives New World Colonization?
There were three major factors for early colonization efforts in the New World: gold, sugar and religious persecution.
The Spanish got into the game first with the gold. By 1535, they conquered both Mexico and Peru and their corresponding gold reserves. Most of the first Europeans to permanently settle the New World did so in relation to one of these two territories, either in their capitals (Mexico City and Lima grew large) at the mines (Potosi in Bolivia grew to almost 100,000 in this time period) or in ports servicing trade to these places (Veracruz, Darien/Panama, Havana, Acapulco).
The second big pull was sugar. There wasn't much good land to grow the stuff in the Mediterranean, and most of that land was in Muslim hands anyways. Already colonized places like Havana and Veracruz were perfect for this crop, as was much of Portuguese Brazil. Once the slaves part of the equation came in to play, this became the perfect high risk/high reward venture for adventurous European lesser nobility. Spend thousands on slaves, hope you don't die of malaria; if you can ship a few tons of sugar back to Europe each year, you will be rich.
The last pull was religious persecution. The Pilgrims of Massachussets and the English Catholics of Maryland are two examples, as were abortive Huguenot colonies in Brazil and Florida and other places. These colonies were the most stable in the long run, since they were by families who intended to stay put, not greedy pillagers and slavers. By the 1700s, the victims of religious wars in Europe were filling the New World: oppressed Scots-Irish; the rest of the Huguenots; German Catholics in Protestant states and Protestants from Catholic states, etc.
In your world, how do you provide the same impetus driving people to plunder, enslave, and/or settle the New World?