Learn Hardcore Korean: hyudaepon baeteoriga ppareuge jureodeureoyo.

The subject is the whole noun phrase 휴대폰 배터리 (phone battery), and the subject marker -가 attaches to the head noun 배터리. 휴대폰 is just modifying 배터리 (like “phone battery” in English), so you get 휴대폰 배터리가 ….

Can I say 휴대폰의 배터리가 instead? When would I use 의?

Yes: 휴대폰의 배터리가 … is grammatically fine and sounds a bit more formal or explanatory. In everyday speech, Koreans usually drop 의 in N+N relationships when the meaning is obvious, so 휴대폰 배터리 is more natural.

Why is it 이/가 here? Could I use 은/는 instead, and what would change?

You can use 은/는 to topicalize: 휴대폰 배터리는 빠르게 줄어들어요. That shifts the focus to “as for the phone battery,” often implying contrast (e.g., compared to other phones or other parts). 이/가 simply marks the grammatical subject without that topical/contrastive nuance.

Why isn’t there an object marker (을/를)? Isn’t the battery what’s changing?

The verb 줄어들다 is intransitive (“to decrease, diminish”), so there’s no direct object. The battery itself is the subject undergoing the change: 배터리가 줄어들어요. If you used a transitive verb like 줄이다 (“to reduce”), you’d need an object: 배터리 사용을 줄여요 (“I reduce battery usage”).

Is 줄어들다 the most natural verb for batteries? Should I say 닳다 instead?

For batteries, the most idiomatic everyday verb is 닳다:

배터리가 빨리 닳아요. (The battery drains fast.)
줄다/줄어들다 also work, especially with words like 잔량 (“remaining amount”):
배터리 잔량이 빠르게 줄어들어요.
More formal/technical alternatives: 소모되다 (“to be consumed”): 배터리가 빨리 소모돼요.

What’s the breakdown of 줄어들어요?

줄다 (to decrease) + -어
- 들다 → the compound verb 줄어들다 (“to decrease, diminish”).
Polite present -어요 → 줄어들어요.
The stem vowel ㅜ takes -어- (not -아-), so 줄다 → 줄어-. This isn’t irregular.

Does this mean “is decreasing right now” or “decreases (in general)”? How do I make it clearly progressive?

Korean present -어요 can be either general/habitual or present/progressive depending on context. To be explicitly progressive, use -고 있다:

휴대폰 배터리가 빠르게 줄어들고 있어요.
Past: 줄어들었어요; future: 줄어들 거예요.

What’s the difference between 빠르게 and 빨리 here?

Both mean “quickly,” and both fit here.

빨리: more common and colloquial.
빠르게: the -게 adverb from 빠르다, a touch more formal/literary.
You can say 배터리가 빨리/빠르게 줄어들어요. Another common adverb is 금방 (“in no time”): 배터리가 금방 닳아요.

Where should the adverb go? Can I put 빠르게 at the end?

Most natural is right before the verb: 휴대폰 배터리가 빠르게 줄어들어요.
Fronting for emphasis is possible: 빠르게 휴대폰 배터리가 줄어들어요 (less common).
Putting it at the very end (… 줄어들어요 빠르게) sounds awkward.

What politeness level is this, and how do I adjust it?

줄어들어요: polite informal (해요체).
Casual: 줄어들어.
Formal polite (reports/announcements): 줄어듭니다.
All combinations are fine: 휴대폰 배터리가 빠르게 줄어듭니다, etc.

How do I ask this as a question?

Use a question mark and rising intonation: 휴대폰 배터리가 빠르게 줄어들어요?
You can also ask with -나요 (softer, curious): … 줄어드나요?

What’s the difference among 줄다, 줄어들다, and 줄이다?

줄다: intransitive “to decrease” (simple statement).
줄어들다: intransitive compound emphasizing the process/degree of becoming less (often a bit more formal or descriptive).
줄이다: transitive “to reduce (something).”
Examples:
배터리가 줄어요/줄어들어요.
배터리 사용을 줄여요.

Any especially natural alternatives for everyday speech?

휴대폰 배터리가 빨리 닳아요. (very idiomatic)
배터리 소모가 빨라요. (battery consumption is fast)
배터리가 금방 다 돼요/금방 꺼져요. (“dies quickly”)
배터리 잔량이 빨리 줄어요/줄어들어요.

Pronunciation or spelling tips?

배터리 is spelled with ㅐ: don’t write “베터리.”
빠르게 starts with tense ㅃ (stronger “p” sound).
In 줄어들어요, the vowels -어- are the “uh” sound; don’t compress it to “주러.”
Colloquial synonyms for 휴대폰: 핸드폰, 폰; formal: 휴대전화.

How can I negate or intensify the statement?

Negation: 휴대폰 배터리가 빨리 줄어들지 않아요. / 안 빨리 줄어들어요 (more colloquial structure: 빨리 안 줄어들어요).
Intensify: 정말/너무 빨리 줄어들어요. (Note 너무 can imply “too/overly.”)