Я поняла, что мне стоило хранить стиральный порошок в кладовке, потому что на балконе он намок.

Because Russian past tense verbs agree with the subject in gender and number.

• поняла = past tense, feminine, singular (speaker is female)
• понял = past tense, masculine, singular (speaker is male)
  If the speaker’s gender is unknown, you’ll often see the masculine form as a “default” in some contexts, but in normal personal speech you pick the form that matches the speaker.

The comma separates the main clause from a subordinate clause. что introduces a content clause meaning that:

• Я поняла, что… = I realized that…
  Russian almost always uses a comma before что in this structure.

мне стоило + infinitive is a common way to express I should have / it would have been better for me to… (often with mild regret).
It’s less like strict obligation and more like hindsight advice.

• Мне стоило хранить… = I should have kept/stored…
• Я должна была… can sound more like duty/obligation: I was supposed to… / I had to…

The construction (кому) стоило + infinitive takes the person in the dative:

• мне = “to me / for me” → “for me, it would have been better…”
  So мне стоило literally aligns with “it was worthwhile/advisable for me to…”

стоило is past tense, neuter singular of стоить. In the expression (кому) стоило + infinitive, the verb often behaves like an impersonal construction:

• Мне стоило… ≈ “It was advisable for me…”
  Because it’s not agreeing with a specific subject like я, it commonly appears in neuter singular (стоило).

хранить is imperfective, and it fits the idea of ongoing storage/keeping something in a place as a general practice.
Perfective options would shift the meaning toward a one-time completed action:

• хранить = to keep/store (as a habit/ongoing state)
• сохранить = to save/preserve (often “save from harm” or “keep successfully”)
• положить (perfective) = to put (one-time action), which would mean “I should have put it in the pantry (at that time).”

It’s the direct object of хранить (to store/keep), so it’s accusative.
For inanimate masculine nouns, the accusative is usually the same as the nominative:

• nominative: порошок
• accusative (inanimate): порошок
  If it were animate masculine, the accusative would match the genitive (e.g., вижу брата).

Both are location phrases answering “where?”, so they take the prepositional case:

• в кладовке = in the pantry/storage room
• на балконе = on the balcony
  Choosing в vs на is partly spatial logic and partly convention. Balconies are typically conceptualized as an “open platform/surface/area,” so Russian commonly uses на балконе (and на балкон for “onto the balcony”).

потому что introduces a reason clause (because), and Russian normally separates it with a comma from the main clause:

• …, потому что … = “…, because …”
  This is standard punctuation for subordinate clauses.

намок is past tense, masculine, perfective of намокнуть = “to get wet (as a result)”. It focuses on the result: it ended up wet.
Comparisons:

• мок (from мокнуть) = “was wet / was getting wet” (state/process, imperfective feel)
• намокал = “was getting wet (repeatedly/over time)” (imperfective past, process)
  Here, намок fits because the speaker is explaining the outcome: the detergent got wet.

Word order is fairly flexible, but it changes emphasis. The given sentence is natural and neutral. For example:

• …потому что он на балконе намок puts extra emphasis on where it got wet (on the balcony).
• …что хранить стиральный порошок мне стоило в кладовке… is possible but sounds more stylized; it foregrounds the action хранить.
  In everyday speech, the original order is clear and typical.

Yes, with small meaning/style differences:

• Я поняла, что… is the most direct “I realized that…”
• Я поняла это, потому что… = “I realized it because…” (sounds like you already mentioned “it” or will summarize it)
• …что надо было хранить… is another common “should have” phrasing; it’s a bit more straightforward and less like the specific стоило nuance of “it would have been better.”