Yes, I
am talking about simply reducing the size of an image, by using interpolation.
NOT redrawing anything.
But instead of a transform (CTR+T), it's much safer to use
Image > Image Size and scale the entire document. This way, your CTRL+T transforms don't fall in between pixels and cause unnecessary blurring.
Both of your examples - the small icons and the diagonal lines should both be drawn with vectors to ensure maximum edge control/crispness. Easy solution.
Especially those icons. You should almost never draw stuff like with the pencil tool, or any other raster tool. Vector is what you need. I draw this sort of thing in Illustrator, then bring it into Photoshop later. I hate Photoshop's vector tools.
If vector, all edges will stay crisp no matter what. And if you carefully control your paths, you'll have ZERO anti-aliasing on straight lines.
Look at this:
Four high quality icons. Drawn in vector. All lines are snapped to the pixel grid.
So, that would solve your silhouette icons problem.
As for your diagonal lines example you posted above, I think it looks just fine. Your final result isn't blurry and there are no sharpening halos.
But here's the problem - both your silhouette icons and your diagonal lines only need to be drawn in vector to be high quality. This is NOT how you'd go about creating the examples you included in your first post. Except for the bullhead, those small images are most likely going to be 100% raster.
In this case, just do like I've already described - start big, then scale down and clean up if needed.