User blog comment:GodKingReiss/Unofficial Timeline/@comment-26932251-20160109035816/@comment-27441457-20160112230655

This is how the book explains Titans climbing the wall:

"Getting up and down the wall was mostly done via a system of ropes, pulleys, and gondola lifts. But perhaps some districts featured staircases, and that was how the Titans had found their way up. Not that they'd actually decided to 'use the wall to cross into another district' - they weren't intelligent creatures. They must have wandered up by chance sometime during the last six months and just carried on walking in search of people, until they happened upon Quinta."

No rules of AOT were broken per se, but it's definitely a big stretch.

As for how they sustained food, Rita set up a "Night Harvest", a periodic event where supervised citizens were sent out of the district to gather fruits and abandoned supplies from Wall Maria's territory under the cover of night, returning to Quinta in the morning with the spoils.