"A texture atlas is a large image containing a collection, or "atlas", of sub-images" - So basicly since we have sub images we will need sub rectangles.
Depending on what you want to do, the engine you use you would use this in diferent sections.
For example, in my engine I do something like this
SubRect is the section of the atlas I want , My Atlas is 100*100 I want the the piece that stays at (50,50) and is 10 Width and 10 Height,
So my sub rect is equal to (50,50,10,10). this says to my engine to "slice" that part and render it a Position coordinate.
From the look of your answers you need to learn a few things before.
You lack knowledge on game design.
Either way, adressing your second question,
To manipulate each sprite as independent object, you would have a abstraction class called GameObject in my case, which has a Sprite associated.
So when I loop through my objects and draw them I actually Draw the Inner Sprite at the Object position, this way I can do what i want with my Objects and they will be aligned to their sprites.
Hope this helps!