mazu genkan no hako wo naka ni hakobu.

の links nouns and can show association or location. 玄関の箱 means “the box at/by the entryway” (i.e., the box located there). If you want to express origin (“from the entrance”), use 玄関から:

• 玄関から箱を中に運ぶ = “Carry the box from the entrance to the inside.”

Not quite.

• 玄関 (げんかん): the entryway/foyer of a house or apartment (inside area by the front door).
• 入口 (いりぐち): the entrance to any place (store, park, building, etc.).

It can be natural if you mean “a box associated with the entryway.” For a delivered parcel by the door, 玄関先 (“just outside the front door”) or 玄関の前 is more idiomatic:

• 玄関先の箱を中に運ぶ
• 玄関の前にある箱を中に運ぶ
• Or specify existence: 玄関に置いてある箱を中に運ぶ

You can, but you’ll lose the “inside” destination. Options:

• Keep it general: 箱を運ぶ (“carry the box”).
• Specify a place instead of 中: 家に運ぶ, 部屋に運ぶ, リビングに運ぶ.
  If you want “inside,” use 中に or be explicit: 家の中に.

Different focus:

• 入れる = “put/place into,” focusing on insertion.
• 運ぶ = “carry/transport,” focusing on moving it.
  A very natural choice is the compound verb 運び入れる (“carry in/into”):
• 箱を家の中に運び入れる.

Japanese often omits the subject. Depending on context, it could be “I/we” (plan or diary) or an instruction to “you.” In manuals and lists, the plain form 〜する often functions like a step/imperative. Polite or explicit versions:

• まず、玄関の箱を中に運びます。 (polite)
• まず、玄関の箱を中に運んでください。 (request)

で marks the place where an action occurs. 玄関で運ぶ would mean “carry (it) in the entryway,” not “from there.” To show origin and destination, use から and に/へ:

• 玄関から箱を中に運ぶ.

There’s some flexibility, but the default is object before destination:

• Default: 玄関の箱を中に運ぶ.
• You can front the destination for emphasis: 中に、玄関の箱を運ぶ (okay in speech/writing with a pause).
  Avoid scattering elements in a way that’s hard to parse.

Standard Japanese doesn’t use spaces between words. Write it as:

• まず、玄関の箱を中に運ぶ。
  Spaces are sometimes used in learning materials only.

Both can mean “inside,” but:

• 中 (なか) is the default for physical inside.
• 内 (うち) is more formal/abstract or group-internal; うち also means “our home/our company.”
  For “carry inside (the house),” use 中: 家の中に.

Natural options:

• まず、玄関先の荷物を家の中に運ぶ。
• まず、玄関の前に置いてある箱を家の中に運ぶ。
• まず、宅配便の箱を家の中に運ぶ。

まずは adds a slight “to start with/for now” nuance and can sound a bit softer or topic-like:

• まずは、玄関の箱を中に運びます。 (polite, soft lead-in)
  Both are fine at the start of step-by-step instructions.

Use a sequence connector such as それから or 次に:

• まず、玄関の箱を中に運ぶ。それから、開ける。
  Polite: まず、玄関の箱を中に運びます。それから、開けます。