You write about English: There is a subtle difference

The same in French.

Que te reste-t-il encore à faire implying that you have already done a part of what you had to do. When

Que te reste-t-il à faire implying nothing about the amount already done.

Some care should be taken anyhow. Depending on the context, the relationship with the speaker, the tone, encore can carry a subtle amount of polite (because implicit) irritation.

If you are late or, on the contrary, if one considers that you already made more than enough… and hear Que te reste-t-il encore à faire ?, this could be interpreted as a reproof.

A Qu’est-ce qu’il te reste à faire?

1.No, the concept “still” (encore) is not necessarily implied; it depends on the point of view. You can say “Qu’est-ce qu’il te reste à faire?” or “Qu’est-ce qu’il te reste encore à faire?” (or alternatively “Qu’est-ce qu’il te reste à faire encore?”); therefore, it can be expected that there is a difference; really, most often, there will be no difference in the context; one will say either to mean “what is left”; that is understandable as the verb “rester” is defined as follows;

(TLFi) Être encore présent, disponible; subsister.

There is a case of a hardly detectable pleonastic usage that, however, someone aware of the subtlety might prefer to avoid and say rather “Qu’est-ce qu’il te reste à faire?”.

2.Nevertheless, in this particular context where the matter that concerns the persons speaking is various things that are still left to do, after having mentioned a few of these things that haven’t yet been done, a question about whether there are still more things left to do is explicit only if “encore” (still) is used.

example

— Qu’est-ce qu’il te reste à faire?
— J’ai beaucoup de choses à faire, faire la vaisselle, faire les lits, faire les courses, et ce n’est pas tout…
— Qu’est-ce qu’il te reste encore à faire?

In that particular context, instead of “encore” the speaker can say “en plus” or “en plus de ça”.

B Est-ce qu’il te reste à préparer le gateau?

The principle in « A1 » applies to this sentence.

C No, “encore” shouldn’t be omitted if the meaning of “still” is to be retained in the first French sentence (J’ai ENCORE mes courses à faire.); in the second, since the verb “rester” is used and in the light of what’s been sais in « A1 » above, “encore” can be omitted.