Mending waist on pants by hand. What's the best me Sewing Machines Parts and Sales in Los Angeles

I just stitched my first “thing” yesterday and feel empowered but don’t know anything about sewing, had to google a bunch of stuff for reference.

I can’t figure out how it was constructed, the outside is black thread while the inside is white which looks like some fancy machine work. It looks like the waistband sewn together before being assembled with the rest of the pants.

Is there a way to make it look like factory or should I backstitch in the shape of an “I” to cover all the seams? Is there a method to ensure the existing stitches don’t unravel further?

I also want to try my hand at fixing the crotch in these two pairs of pants but adding extra stitching doesn’t look like it’d work.

Pics of inside and out:
http://i.imgur.com/KWEM5py.jpg?1
http://i.imgur.com/m2xT2KY.jpg?1

Worn out crotch that needs fixing:
http://i.imgur.com/XSO2RX4.jpg?1