Learn Hardcore Japanese: hako ha genkan ni oite aru. - The box has been placed at the entrance.

It marks 箱 as the topic: “As for the box…”. Using は implies the box is known or previously mentioned, or you’re contrasting it with something else. It tells the listener the sentence will say something about the box.

Why is に used after 玄関 and not で or へ?

に marks the location where something exists or ends up (result location). With ある/いる and with 〜てある, you use 場所＋に.
で marks the place where an action happens; it’s not used with ある or 〜てある, and 置く specifically uses に for the destination of placement.
へ marks direction (toward), not location; you can’t say 玄関へ置いてある.

What exactly does 置いてある mean?

It’s the te-form of the transitive verb 置く plus ある. 〜てある describes a current state that resulted from someone’s intentional action: “(has been) placed and is there now.” The agent (who placed it) is not mentioned.

How is 置いてある different from 置いている?

置いてある = resultative state of a completed, intentional action: “is (has been) placed.”
置いている with 置く usually means someone is in the middle of the act of placing or habitually places it there. It’s not used to describe the state of “it is placed.” So say 箱が/箱は玄関に置いてある, not 箱が玄関に置いている.

Why is ある used instead of いる?

ある is for inanimate things; いる is for animate beings. Also, the pattern 〜てある always uses ある because it describes the state of an (inanimate) object after a deliberate action.

Can I use が instead of は? (箱が玄関に置いてある)

Yes. 箱が玄関に置いてある presents “a box is placed in the entrance” as new/neutral information. 箱は玄関に置いてある topicalizes the box (known/contrastive). Roughly:

Q: “What’s in the entrance?” A: 箱が玄関に置いてある.
Q: “Where is the box?” A: 箱は玄関に置いてある.

Can I drop 箱 and just say 玄関に置いてある?

Yes. If context already makes the topic clear, 玄関に置いてある naturally means “(It) has been placed in the entrance.”

Why isn’t を used with 箱 here?

In 〜てある, the thing that was the direct object of the original action becomes the grammatical subject/topic of the resultant state. So instead of the action sentence 箱を玄関に置く, the resultative sentence is 箱が/箱は玄関に置いてある (not を).

Does 箱 mean “the box” or “a box”?

Japanese has no articles. 箱 could be “a box” or “the box.” Using は tends to imply a specific, already-known box.

What exactly is 玄関?

玄関 (げんかん) is the entryway/foyer of a home or building—the area just inside the front door where shoes are removed. It refers to the inside entryway, not the outside doorstep.

How do I make this polite, past, negative, or a question?

Polite: 箱は玄関に置いてあります。
Past (plain): 箱は玄関に置いてあった。
Past (polite): 箱は玄関に置いてありました。
Negative (polite): 箱は玄関に置いてありません。
Negative (casual): 箱は玄関に置いてない。
Question (polite): 箱は玄関に置いてありますか。

How is this different from 箱は玄関にあります?

あります is plain existence: “The box is in/at the entrance.” 置いてある adds the nuance that someone placed it there on purpose and it remains there.

What about 置かれている? Is that okay?

置かれている is the passive: “is placed/being placed.” It describes a state too, but sounds more objective/formal and doesn’t carry the same “intentionally arranged” nuance. For everyday “It’s been placed/left there,” 置いてある is more natural. Avoid 置かれてある (ungrammatical/redundant).

What other verbs commonly use 〜てある?

Many transitives:

ドアが開けてある (someone has opened the door and it’s left open)
ポスターが貼ってある (a poster has been put up)
椅子が並べてある (chairs have been arranged)
ご飯が用意してある (a meal has been prepared)
メモが机に置いてある (a note has been placed on the desk)

How flexible is the word order?

Very flexible. All of these are possible with nuance shifts:

箱は玄関に置いてある (topic = box)
箱が玄関に置いてある (new info)
玄関に箱が置いてある (focus on place first)
玄関には箱が置いてある (topic = entrance)
玄関に箱は置いてある (contrastive “at the entrance, at least the box is there”)

What nuance does 玄関に箱は置いてある have?

It’s contrastive: “In the entrance, at least the box is there (maybe other things aren’t).” Example: 玄関に箱は置いてあるけど、バッグはない。

How do I ask “Where is the box?” using this pattern?

Neutral: 箱はどこにありますか。
With the “placed” nuance: 箱はどこに置いてありますか。

How is 置いてある different from 置いておく?

〜ておく describes the action done in advance/for a purpose: 箱を玄関に置いておいた = “I put the box in the entrance (ahead of time).”
〜てある describes the current result state: 箱は玄関に置いてある = “The box is (has been) placed in the entrance.” The first focuses on what someone did; the second on how things are now.