1) You could install a simple metal roof with drainage and a gutter under the terrace on the roof of the shed, but it would look nicer to roof the terrace so that almost no rain comes onto it. Then it should be enough to screw up some fiberboard panels or similar in the shed ceiling.
2) You can leave an air gap of 5 cm to the paving stones, but build up a threshold inside of 10 cm. This should give you decent air circulation without water getting into the shed. Ideally, use horizontal paneling as the bottom one will have a shorter lifespan than the others.