What word names a small cave, like the famous "blue one" on Capri?

What word names a small bit of snow, soap or cereal? What word for a bell tower is proverbially home to bats? What small cap is worn over the fingertip for protection while sewing? What word names a small car or a small mirrored makeup case in a handbag? A small chapel in a village northwest of Moscow marks the source of which river, more than 2,000 miles long? What is a small cucumber preserved in vinegar or brine called? A small, dim star such as Proxima Centauri is called what? What French word describes a small, tender filet of beef?