Is it possible to group several objects and then manipulate them (scale, rotate, translate) as one? I've never been quite able to figure out how groups work in Blender (at least not since 2.5/6x). Is it possible to group several objects and then manipulate them (scale, rotate, translate) as one?
Groups in itself are not that useful. You cannot directly manipulate a group of objects as one object. Although groups make it easier to select objects with Shift + G.

The real power of a group comes from instancing and dynamic linking. Which I will explain:

Instancing:

Once you've created a group, you can instantiate this group elsewhere in the scene by Add>Group Instance. This saves you the trouble of creating literal duplicates of your objects. Consider a city scene, I might have a number of objects that makes up a car model. By grouping these objects into a group, I can place a car group instance anywhere in the scene with very little overhead.

Dynamic Linking:

In many ways, dynamic linking is an extension of instancing. The only difference is that we are using a group from another blend file(often called a library). Dynamic linking is a very useful feature in a large production, because it allows larger scenes to be broken up in smaller chunks. (managed by different people)