Light, shadow, and colour are your answers. All those things can be used to separate one form from another. There will always be variations in lighting and colouring, even across a face (there's a lot of colour variance in a face). It's important to look at real objects and see what it is that defines there shape and separates them from objects around them, and how light changes things.

Nothing says you have to completely get rid of lines either, but you can always just paint over them. 

Well, it's very easy. You draw lines first for your edge control. Later, you fill the right colors in and make the lines disappear. Result: clearly-defined edge without lines.

Regarding your question about large brush ruining the rest of your painting, I think it's more about th method you paint. Usually, you use large brushes to define tones and shapes, like the information of light and shadow, so this is the stage where you do not worry about "messing up other parts" because every part of the painting is just as rough, which is the idea. You only need to worry about ruining the other parts when you start to define the details, and by that stage you will most likely be working with a small brush and it would be easy to control them.

If you paint by rendering each and every little area, that's probably okay, too. But that's usually not very efficient and you could easily lose control of your overall image.

If I might offer a couple thoughts...

"Refining the edges" can be interpreted in a number of ways. As far as I understand it, edge refining is mostly applicable for artists who paint images that were not begun from a fleshed out sketch or piece of line art with all its forms defined..

Without the use of a sketch, that way the technique is to simply paint down blobs which then get constantly sculpted and shape refined (edge-refined) to better represent the features and forms that are trying to be illustrated.

Even when you're painting up from a sketch or piece of line art, it also really depends on how much you've predefined in that sketch and how much you're leaving to your imagination to create and fill in as you paint.

To edge refine, it can involve the use of an eraser to remove excess paint from a form that has too much mass, or it could also mean the application of further layers of paint to embellish the visibility of a particular form, contour or outline. 

It really depends on context.

Images of your work at a particular stage could really help us out in terms of helping you out in understanding better.