Rome's legions almost always were vastly outnumbered, but their tactics, weapons, and training allowed them to win, at up to 10-1 ratios. There was noting equal about the two forces. The Legions had only one decisive loss, to Germanic troops in a clever ambush, in the Tuetoberg Forest.
About questions 2 & 3, who knows. Probably the Persians and Spartans due to their discipline and tactics. Samurai fought individual battles, although they had much better armor protection. Any disciplined unit always defeats an uncoordinated attacker. It is much more probable that Spartans would beat Vikings because armor and spears are superior to leather with swords or axes, discipline beats berserk attacks, and Spartans too had their fearsome appearances.
4. Easily the Mongols.Their (recurved) compound bows had double the range of the longbow, and half-again as much power. Mongol soldiers are reputed to have had a range up to 1.000 yards, equal in distance to a modern combat rifle. More decisively, Mongols preferred to fight on horseback, running circles around their enemies, and attacking in ebbs and flows in order to disrupt enemy positions/units. It would be a slaughter of the English to attempt such a contest.
Results: Roman armies, elite Persian units, Spartans, and Mongols would prevail--as they did in their own battles, mostly.