Drop bars get the hanholds a bit towards the front - very much like the handhold on the mounted horns you depicted.
If a bicycle's frame is the right fit for your height and torso&arm length, then swapping its flat handlebar for a drop bar may require using
compact drop bars and a
shorter stem.
Or, a longer stem, if it already is a drop-bar bicycle, and you wish to swap drops for a flat bar.
Past a certain point, you will need to look for a smaller frame, or a frame designed for drop bars (shorter top-tube to compensate for the drop bars sticking further to the front, bluntly put).
Regarding brakes, there are several options:
- Mount mechanical disc brakes for road bikes (like Avid BB7-R - Amazon affiliate link).
Those work with normal rim-brake drop bar levers.
- Mount V-brake levers for road bikes (like TEKTRO RL520 - Amazon affiliate link).
Those would allow you to use any MTB mechanical disc brakes (more common, easier to find), but those levers are just for brakes, you would need separate shifters (see here for different road bike shifters explained).
- Get hydraulic STIs and matching hydraulic road bike disc brake calipers.
This is an expensive option.
Such projects may sound simple. They can be very fun. But they require some knowledge, experience, and trial and error. I've already covered most of the problems and dilemmas you may face in my articles and videos.
Compatibility series - to name one.
I would also recommend using the
full search - it could give you pretty good instant answers for most questions.