re: How many undefeated and perfect seasons has your football program had?

College football wasn't really "organized" till about 1906 (when the precursor to the NCAA standardized the rules and such). Prior to then different parts of the country played with different rules, slightly different scoring systems, stuff like that.

Pretty much all college football played in the 1800's was glorified intramurals, essentially like a club sport is today.

Alabama for example sometimes played high schools or things like freaking fire/ambulance department to even have opponents to play. That's why a lot of teams have mostly 2-5 game scheduled back in the early days. Some schools even played the same opponent 2-3 times in the same year.

By the early 1900's college football had grown to the point it was a national phenomenon and there was an interest in turning it a coherent sport, which is why the first conferences and bowl games began appearing about then too, and you'll notice almost everybody from then on had a full schedule (7-8+ games).