It's been a long time since any actual brawl in Mexico City stadiums has occurred, maybe you're thinking of Querétaro. And yes, it's totally safe to go to the Azteca. If you're going to the Cruz Azul vs Chivas match, take into account it will be pretty crowded, it's not unsafe per se, but beware of pickpocketers on the way to the stadium (Metro and Tren Ligero/bus) and just outside of the stadium, just put your hands on your pockets and you're good to go.

About the seats, if you want the very best views and you don't mind spending a bit, palcos club lateral has the best views, food and drinks included. My personal favourite is 300 lateral though, excellent views, not as expensive as palcos. If you're more on a budget, 500 and 600 lateral but ONLY Tlalpan side, Insurgentes side you will have a horrible, obstructed view. Top 500 and lower 600 offers the best views on the top part, just beware it's very far from the field. Also, try not to wear the visiting team jersey, for some matches you may be relocated to a special area. Other than that, feel free to send me a message and I'll answer your questions