ことが and ことは

Basically, yes, the "wa" in the second case shows contrast, and, generally, in a negative sentence, "ga" can change to "wa".

In the first sentence, the "ga" is used to mark the subject, being the "drinking" of the sake. However, the emphasis is on the implied "Anata wa", as in:

As for YOU, have ever drank sake?

In the reply, the "ga" changes to "wa" to place the emphasis on the "drinking", ie.

No, (I) have never DRANK sake.

This implies that the responding person may have had prior knowledge about sake, but has never actually, drank sake.

The "wa" is contrastive. For example, Kutsu o kaimasu > Kutsu wa kaimasen.

General Idea: when "ga" is present in a negative sentence, change it to "wa".

Yes, -kute is used when listing adjectives. The usage in the lesson, atatakaku te mo
tsumetaku te mo... Also uses the mo...mo.. construction which is used to mean both or either.

So its: both warm and cool/ either warm or cool.

It can also be used with nouns.
Eg. Sakuya-san wa, sushi mo tenpura mo suki da ne? Ms. Sakuya likes both sushi and tempura doesn't she?

Note, the loss of the "ga" in "ga suki da", since the double particle "mo ga" doesn't exist.