"Didn't the Romans win the Battle of Carthage?" Yes, they did, Commodus... but as noted under Artistic License in the main page, the "home team" of chariot riding archers (including women) are about as far removed from the three lines of the Pre-Marian Roman Army. If anything, Maximus and his team were what the actual Romans of the era would be (even using a similar shield model painted black). And, by using Roman tactics (formation fighting, aggressively plunging into gaps in the enemy, etc.) they did indeed win the recreation of the Battle of Zama, winning the crowd in the process.
The trees along the path of Maximus' home? They're cypress. In Roman mythology, the cypress tree was linked to Pluto, the god of the underworld.
Maximus says he will have his vengeance "in this life or the next." He ends up getting both by killing Commodus and returning control of Rome to the people at the very end of his life and, after succumbing to the injury Commodus inflicted before his fight with him, he is able to return to the family that Commodus had murdered.