Question

When is it obligatory and when is it not? When does it prevent the recitation of blessings, Torah study, and prayer? Is this purification from impurity, or only an added level of purity? If someone mistakenly recited a blessing without a kippah under the open sky, does he repeat the blessing? Because when there is a ceiling, I heard that one does not repeat it, since there is an opinion that the ceiling is considered a head covering.