Question

Immanuel kant believed that it is only when we act out of feeling or sentiment that our actions have moral worth

Answer 1

It is false. Kant's theory is an example of a deontological moral theory - according to these theories, the rightness or wrongness of actions does not depend on their consequences but on whether they fulfill our duty. 
Kant believed that there was a supreme principle of morality, and he referred to it as The Categorical Imperative.