Except we've had plenty of examples of Westernized Muslims. Turkey is a secular government run by and a country mostly populated by Muslims. Beyond that, the Muslims you find in Western cultures, in fairly short order, support Western institutions. To keep out people because of their faith would be so contrary to our principles as a country of immigrants who often left their native lands to escape religious persecution and proscription as to undo something integral to our character as a people.
You have to distinguish between sudden influxes of refugees with normal immigration.
Corporations will love you, but we managed one of our greatest industrial boom periods during a time when corporate taxes were higher than they are now. The problem is greed, not taxes. And there's another way to handle it. Put a cap on profits. If the captains of current industry don't care for it let them go elsewhere and I promise you there will be ample replacements who will find being rich sufficient motivation.
The government isn't. And the rich pay laughably low taxes, on average lower than the middle class. That said, if you want the rich to pay their fair share tax luxury goods. Consumption taxes (not on essentials) can fill the coffers and put a lot of tax attorneys out of business. A win/win.
Sure, though those have to be fair for everyone and not merely better for the other guy.
You think they'll be surprised? An alliance with a country containing its resources makes a great deal of sense, provided we can trust them or failing that have sufficient verification that they'll live up to their end of an economic alliance.