Drop-to-flat and flat-to-drop are both common questions here.
A search should yield plenty of reading material.
You can keep the brakes, but you will need to pick the right kind of brake levers.
Drop bar levers need to sit on the outside face of a fairly sharp bend to work, and not many flat bars fit that description.
Shifters can be tricky or dead simple.
Finding integrated shifters/brake levers to match the current drivetrain - which you don't say what you have - can be tricky.
Stem or downtube shifters are easy.