Non-inverting op amp on breadboard isn’t working

Yes it looks quite safe (providing you don't connect up anything badly on the breadboard of course)
The jumper cables are physically the same, just the colours are usually used to denote different rails/signals to make it easier to remember what is what (or on a wiring diagram the colour/signal relationships would be noted to enable someone to find the required signal easily)
Often you might use e.g. red for +V and black for -V, but you can use them as you wish.

1) Physical breadboards are available with core sections and bus sections as individual dockable modules, so the arrangement you show is realizable but my personal preference would be for a pair of bus row on top and bottom as well.

2) Spacing seems to be right for the core module, should be 300 mills or 3 units between top and bottom halves. However the spacing on your bus rows is different than the physical example in front of me, which has 5 holes lining up with those in the core, then one missing, then another 5, etc. The spacing across the gap to the bus row is also 300 mill.

3) I'm not sure I'd say confusing, but the color choices and graphic thicknesses induces eye strain. Consider taking a photo and more closely duplicating that with more shades of color.

Reading your question I immediately wondered if you know about http://fritzing.org/ - at the least, check it out and identify in your own mind the reasons why your open source effort should be separate from theirs. You don't have to post your conclusions, but if you decide to remain distinct thinking about how yours would be better may provide some useful guidance.