What is the difference between 还是 and 还?
OP already listed their different definitions. They don't seem to be interchangeable at all.
The meaning of 'still' may be the only one where either word-choices can be used in the same sentence, but there's still some subtle differences between them:

Fact 1 + 还 + Fact 2 describes the facts without emphasizing any.
Fact 1 + 还是 + Fact 2  emphasizes the seriousness of Fact 1: despite Fact 1, Fact 2 still occurs .

Examples:



水浸眼眉了他还不逃命.
His eyebrows are flooded and he won't run away.

Describes a situation without emphasizing any part: Fact 1. 水浸眼眉了 and Fact 2. 他还不逃命.

水浸眼眉了他还是不逃命.
His eyebrows are flooded, he still won't run for his life.

Emphasizes the seriousness of 水浸眼眉: despite 水浸眼眉了, 他还是不逃命.



天黑了还不回家.
Not going home when it gets dark.

Describes a situation without emphasizing any part: Fact 1. 天黑了 and Fact 2. 还不回家.

天黑了还是不回家.
Still not going home after dark.

Emphasizes the importance of 天黑了: despite 天黑了, he still 不回家.