It has a stop motion animation feel to it.
With standard keyframes, motion is interpolated between two points smoothly.
The 'stop motion' effect is achieved by using hold keyframes instead.
How are they animating the text
Usually the answer to these questions are keyframes, lots and lots of keyframes. Specifically keyframes on scale, position, rotation and occasionally opacity.
The timewriter effect applied to individual characters or words can be easily achieved in After Effects using the 'Animate Text' effect.
The subtle 3D text effect at 00:35 can be achieved using the 'Basic 3D' effect. In the current version of AE the effect is listed as obsolete but it's easy to use.
Also most of the text are used as masks on top of photographs to add a texture.
How are they doing the rotate in and out transitions (Are they
rotating in the entire precomp file?)
It's likely that individual elements such as text and images are being rotated individually with the rotation offset of each element at different places.