Text animators are an essential part of working with text in AE, I suggest you read up on them, which you can do here. Text animators give you lots of tools for doing the kind of effects you want, but they're slightly unintuitive. However for the beginner there are dozens of presets included.
As far as the boxes go, it's a fairly simple animating task, that could be achieved with masks, matte layers, animated shape layers, a combination of the above, or probably a dozen other techniques. A good tip is to slow down the video you want to reproduce, and work out what exactly is going on frame-by-frame.
For example the eat less junk food text box starts as a series of boxes which you could create using shapes that have their scale animated, until they overlap and form a single box. Or perhaps you could have a single box that is revealed by a number of masks that are animated to grow.
The box is then split in two which you could achieve with another animated mask using the subtract masking mode that starts with zero width and grows until it covers the box completely. Notice that as this happens the green shape is growing slightly, so you animate its scale as well.
TL;DR: the plugin you need is called Animation™.