Is rainwater weak acid that dissolves limestone and rock and creates caves?

Correct, in limestone including its meta-form marble, and gypsum; respectively calcium carbonate and calcium sulphate. The acidity comes from absorbed atmospheric carbon-dioxide.

NB though: Limestone is a rock anyway, but only these two calcium compound rocks are soluble to any real extent. Dolomite (magnesium carbonate based) will dissolve but the physical nature of its deposits tends to prevent cave formation.

Rainwater will also attack the felspar in granite but the process, hydrolysis, is extremely slow and does not lead to dissolutional caves in granite.