I'll submit child's play as a term that means an easy exercise or task in the context you've given in part 3.

Example: That calculus problem was child's play compared to the functions we're studying in advanced physics.

It also came up on Reverso for Fingerübung with this example:

Mit diesem, auf dem m2webalizer basierenden Produkt von mquadr.at wird die erfolgreiche Einrichtung des Internetzuganges zur lockeren Fingerübung.

With this service product, based on the technology of mquadr.at's m2webalizer, a successful internet setup becomes childsplay [sic].

In English, this term is two words, child's play, referring to something so simple, a child could do it.

I'd say "warm-up problem" or "warm-up exercise" might be a good translation if you're using it in school or college courses.

From Merriam-Webster:

Warm-up: a preparatory activity or procedure.

The expression I would use is no brainer:

If you describe a question or decision as a no-brainer, you mean that it is a very easy one to answer or make.
[informal]

For example, in the book 5 Steps to a 5 AP Microeconomics and Macroeconomics:

Question number one looks like a no-brainer.

A fresh one the last few years in English is easy-peasy.

(Interestingly, it's a fairly old formulation (perhaps from the 1940s?) but it's become a fad lately.)

Here's a kind of taxonomy ...

easiest
 child's play        
 no-brainer        
 easy-peasy        
 warm-up
hardest


more supercilious, the task is a "joke", being critical of the proponent,
suitable for condescension
 no-brainer        
 child's play           
 warm-up  
 easy-peasy  
less supercilious, task is worthy but easier than other approaches,
not used in condescension


less current in teen/everyday language, quaint     
 child's play    
 warm-up  
 no-brainer        
 easy-peasy  
more current in teen/everyday language, popular

A note on (scholastic) "exercise"...

In fact, the OP has (deliberately or not) emphasized that the SWR is an easy-peasy academic exercise, for example a math problem. As opposed to just an easy-peasy "anything".

Two thoughts,

(1) I'm not entirely sure that it is correct that in German the term is "only" used or even "leans towards" application to textbook problems.

{It could be the OP is just wrong (!) or just that the issue was, uh, lost in translation.}

(2) If the OP literally wants an English SWR meaning literally in relation to textbook, scholastic, academic drill problems - the answer is simply that there is absolutely no such term.

(To inject a note of humour, in the English-speaking realm, we don't do academic stuff. It would be like a Japanese asking for a translation of one of their words like "total focus on success!" (nope) or indeed a German asking for a word for "management and unions working together harmoniously!". We don't have that stuff :O )

The most common word for this in English is "Trivial". As in "I finished the trivial questions first."

"Toy problem" or "toy example" might work, and is often used in academic contexts. It's often used to describe a demonstration (such as in a textbook or something presented by a professor), not necessarily something that students would work on themselves, but I think it can be used for either situation.

In short, Fingerübung translates just fine as finger exercise, using it figuratively is awkward/unusual in both languages.

The longer explanation is that you misunderstood the Duden. Fingerübung is not a common term to start with (that's what the 1/5 bars next to Häufigkeit mean) and then it's a specific term from the area of "Musik" which you can find next to "Gebrauch" (usage). Both meanings listed on the Duden page refer to playing instruments, where you are literally practicing finger movements ("finger exercises").

kleines Übungsstück als Fingerübung

translates to something like

short piece of music to exercise the fingers

and not

small/easy piece of an exercise (translation: me)

as you thought. "Übungsstück" is a compound word built from Übung/exercise and Stück/piece of music. The latter is a common abbrevation of Musikstück, it's very clear that Stück doesn't refer to a piece of anything else but music.

Now of course someone might use that figuratively in some non-music context, but that's not the meaning that is listended in the Duden and it sounds kind of awkward - probably exactly as awkward as it sounds to just use the equivalent English finger exercise.

The obvious English expression, used in relation to some sublime piano pieces written by a certain German composer, is actually given in the Duden translation cited in the posters’s question:

Easy pieces

Although it is general used for practice exercises in a musical context (see e.g. here, but a search on Amazon should convince) the expression has been extended as an idiom, as evidenced by its use in the title of the movie “Five Easy Pieces” which some older list members may remember.

N.B.
‘Easy Pieces’ in this context does have a literal German equivalent in “leichte Stücke” (as pointed out by @PeterShor). It is interesting that the German title of the film mentioned does not employ this: “Ein Mann sucht sich selbst” (literally, but inelegantly, “A man seeks himself”).

After reading a comment left by the author on a prospective answer, I believe the closest term would be "low-hanging fruit". It is a problem which is generally termed to be trivial, but still has reward for completing it, and it will generally be completed first as a result. A student on an exam would generally seek out the easier problems on an exam (the low-hanging fruit) first, and then would be likely to attempt more difficult problems after completing those.

As I said in a comment under Nobody's answer I think the figurative use of Fingerübung is idiomatic and expressive, even though the Duden entry (b) is not describing it (but a piece of music written or played for the purpose of exercise, an étude).

It turns out that there is an exact English equivalent, the five-finger exercise, which can be used figuratively as well.

Other suggested translations like child's play or easy-peasy miss the learning or preparatory aspect which is usually present when Fingerübung is used. And if one wanted to express child's play one could use the exact German counter-piece Kinderspiel instead of Fingerübung.

The purpose of Fingerübung might be to learn or to warm-up, either of which builds or refreshes muscle memory. So Depending on what you are trying to say, and especially if you want to retain the idiomatic tone, you might consider using some form of "muscle memory". The concept of warming up or building muscle memory was the first thing to come to my mind when I read your question.

You might have a look at the term "Kata", which is martial arts exercises which you repeat over and over to strengthen muscle memory. Programmers use it as well to repeat a known problem solution in a new language (https://en.wikipedia.org/wiki/Kata_(programming))

The German term might possibly arise from a piano lesson book I used when I was perhaps 12, titled, "Übungen um den Fingern voneinander unabhängig zu machen." That's "Exercises for the fingers from each other independent to make." Parts of it were easy. Other parts not so much, as in this example, "With the right hand hold down C, D, E, and G, and strike F with the ring finger repeatedly." Or similarly, "Hold down C, D, and E, and with the ring and little fingers trill F and G."