Your grip should be firm enough that an unexpected pothole or rock doesn't knock your hand off the brifter. But that should be only the tensing of muscles in your hands, not wrists and forearms. The rest of your arms should be relaxed, even loose (so say another rider bumps your elbow - it would then be no big deal).

There is no magic re: space between your hands and the brifter. Find the best, secure and relaxed positions (plural). And change them often. Also ride the drops. Wind at your back? Sit up and ride the tops. The great thing about dropped handlebars with brifters/brakes on them is that you have so many choices on where to place your hands. The different choices offer more and less secure handholds, elbows in for minimum air resistance, elbows out for maximum breathing and power, etc. Gert to know them all. Observe what other riders do. But above all, find what works for you.

Ben