Seldom do I see a question that is so completely in my flair area! I actually pretty much answered this question two years ago, although the writing's a bit clunky in places. But I can address your more specific points below:

The battle of Legnano was most certainly not a battle against two equivalent sides. Emperor Frederick "Barbarossa" was returning from a meeting with the Duke of Bavaria in the alpine town of Chiavenna; in addition to his bodyguard, he was moving south with only about two thousand Bavarian knights reinforcing him. Although the plan was to link up with the main imperial force in Pavia, the Milanese moved before that linkage could happen. Frederick was probably planning to offer battle in the vicinity of Alessandria, where the the bulk of Lombard fighting men were located and posed an important static threat to his movements in Northwest Italy.

Although it took nearly a decade to emerge, by 1176 the emergence of the Lombard League had not only allowed the Italian Cities to pool their more seasoned fighting men and create a standing threat at Alessandria, but also rally a substantial complementary force of armed citizenry. Knowing Frederick was moving in the vicinity of Varese, the Milanese Consul and Captains rallied some ten thousand burghers hailing from Bergamo, Brescia, Cremona, Mantua, Lodi, and Cremona in order to set out and intercept the Emperor.

This brings us to your second point; although Northern Italy is indeed generally flat, Emperor Frederick was moving south through the densely forested foothills of the Alps. Up to the morning of the battle, his movements had been entirely hidden from the Milanese. In fact, neither side had really planned for the battle to take place the way it did: the Emperor obviously would have preferred to remain hidden all the way to Pavia, while the Milanese had hoped to attack the Emperor as he crossed the river Ticino farther upstream. They had no idea he was already on the near side of the river and moving south.

However, the general set-up was nonetheless favorable to the Milanese. Military doctrine at the time generally stipulated that while the core of infantry engaged in the center, whomever obtained cavalry superiority on the wings would then try to encircle and rout the enemy. The Emperor's force was not only entirely mounted, but with the Ticino on his left flank, Frederick found his right flank limited by the river Olona; this made complex encirclements an impossibility. All the Milanese had to do was stand still and wait for the Emperor to come to them, and that's exactly what they did.

With the Lombard forces barring his way, Emperor Frederick has no choice but to order a head-on charge and hope he cound break through so in order to then sprint to Pavia. Unfortunately, charging straight into a spear wall is a very, very easy way to to lose a battle. Frederick himself was unhorsed and barely escaped with his life.