What is the difference between 还是 and 还? What is the difference between 还是 and 还? Is 还 the short of 还是 and, consequently, they are interchangeable in every situation, only in some cases or never?

For reference, I will list the different situations I have seen them. Can any be expressed both with 还 and 还是？
还:

means still / despite the situation in a negative sentence： Subj + 还 + 不 / 没 + [Verb Phrase]. E.g.:

我解释了这么多遍，你还不懂 ？
Wǒ jiěshì le zhème duō biàn, nǐ hái bù dǒng?
I've explained it so many times, and you still don't get it?


means also: Subj + Verb， 还 + Verb. E.g.:

她有一个弟弟，还有一个妹妹.
Tā yǒu yī gè dìdi, hái yǒu yī gè mèimei.
She has a younger brother and also has a younger sister.


means again: 还 + Verb. E.g.:

这个电影很好，我看过，还想看.
Zhège diànyǐng hěn hǎo, wǒ kànguò, hái xiǎng kàn.
This movie is very good, I watched it before and want to watch it again.


means pretty/fairly: Subj + 还 + Adj. E.g.:

我还好。
Wǒ hái hǎo.
I'm pretty/fairly good.


expresses a strong tone of surprise: Subj + 还 + Predicate + 呢 . E.g.:

还留过学呢，英语这么差 。
Hái liúguò xué ne, Yīngyǔ zhème chà.
You have studied abroad, yet your English is so bad.


marks a rhetorical question: Subj + 还 + [Verb Phrase] + 吗 ? . E.g.:

他说的话，你还听吗？
Tā shuō dehuà, nǐ hái tīng ma?
Did you listen to what he said?


means even more: Noun 1 + 比 + Noun 2 + 更 / 还 + Adj. E.g.:

他比姚明还高 。
Tā bǐ Yáo Míng hái gāo.
He is even taller than Yao Ming.



还是:

means still / despite the situation in an affirmative sentence: ⋯⋯ ，(但是 / 可是 +) Subj + 还是 + [Verb Phrase] . E.g.:

父母不同意他去，可是他还是去了。
Fùmǔ bù tóngyì tā qù, kěshì tā háishì qù le.
His parents didn't agree to it, but he still went.


provides choices in a question: Option A + 还是 + Option B ? . E.g.:

你喝茶还是喝咖啡 ？
Nǐ hē chá háishì hē kāfēi?
Do you drink tea or coffee?


means had better: Subj + 还是 + [Verb Phrase] + 吧 . E.g.:

你还是快点走吧 。
Nǐ háishì kuài diǎn zǒu ba.
You'd better leave now.
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.