tantoubusyo ga mada kimatte inai rasikute, henzi ni zikan ga kakatte imasu.

担当部署 means the department in charge, the responsible department, or the division handling the matter.

• 担当 = in charge of something / responsible for something
• 部署 = department / section / division

So in this sentence, it refers to the office or department that will handle the matter, but that department has apparently not been decided yet.

が marks 担当部署 as the grammatical subject of 決まっていない.

So the structure is:

• 担当部署が決まっていない
• The responsible department has not been decided

Using は would also be possible in some contexts, but it would sound more like you are setting 担当部署 up as the topic for contrast or discussion.

Compare:

• 担当部署がまだ決まっていない
  = The responsible department hasn’t been decided yet.
• 担当部署はまだ決まっていない
  = As for the responsible department, it hasn’t been decided yet.

In this sentence, が sounds natural because the speaker is simply stating the situation.

This is a very common point of confusion.

まだ can mean:

• still with a positive verb
• not yet with a negative verb

So:

• まだ決まっていない = has not been decided yet

Examples:

• まだ食べています = I am still eating.
• まだ食べていません = I have not eaten yet.

In your sentence, まだ + 決まっていない clearly means not yet decided.

決まっていない describes the current state: something has not been decided.

• 決まる = to be decided
• 決まっている = to be in the state of having been decided
• 決まっていない = to not be in that decided state

So:

• 担当部署がまだ決まっていない
  = The responsible department has not been decided yet.

By contrast, 決まらない can sound more like:

• it does not get decided
• it won’t get decided
• it remains undecided

That can be more general or more dynamic. In this sentence, 決まっていない is the natural way to describe the current situation.

No. It is not the passive form.

This is because 決まる is already an intransitive verb, meaning to be decided.

Compare:

• 決める = to decide something
• 決まる = to be decided

So:

• 担当部署を決める = to decide the responsible department
• 担当部署が決まる = the responsible department gets decided / is decided

Then:

• 担当部署が決まっていない = the responsible department has not been decided yet

So even though the English translation often uses a passive-like expression, the Japanese grammar here is not passive.

Here, らしくて means something like:

• apparently
• it seems that
• from what I hear / from what it looks like

So:

• 担当部署がまだ決まっていないらしくて = It seems that the responsible department hasn’t been decided yet, and...

The て form of らしい connects this clause to the next one, so the sentence continues on to give the result:

• ...返事に時間がかかっています
• ...so the reply is taking time

So the whole thing has a cause/result feel: Apparently the responsible department hasn’t been decided yet, so the reply is taking time.

らしい usually means the speaker is not stating a direct fact they know for certain, but is basing it on:

• what they heard
• what they were told
• what seems to be the case

It often sounds like apparently or it seems based on evidence or information.

So the speaker is not saying:

• I know for sure the department has not been decided

They are saying more like:

• From what I can tell / from what I’ve heard, that seems to be the reason

This makes the statement softer and less absolute.

Sometimes yes, but the nuance changes a little.

• らしい: apparently / I hear that / it seems
• ようだ: it seems / it appears, often based on observation or reasoning
• そうだ: I heard that / it seems, depending on the type

In this sentence:

• 決まっていないらしくて sounds very natural for apparently it hasn’t been decided
• 決まっていないようで is also possible, and can sound a little more analytical or observational
• 決まっていないそうで would sound more like I heard that it hasn’t been decided

So they are related, but not identical. らしくて is a nice natural choice here because it sounds like the speaker is giving a likely explanation without sounding too definite.

Because 時間がかかる often uses に to mark what the time is spent on.

Pattern:

• A に 時間がかかる
• It takes time for A / A takes time

So:

• 返事に時間がかかる = it takes time to reply = the reply is taking time

Other examples:

• 準備に時間がかかる = preparation takes time
• 修理に時間がかかる = repairs take time
• 説明に時間がかかる = explaining takes time

So 返事に means for the reply / in replying.

These are different expressions.

• 時間がかかる = time is required / something takes time
• 時間をかける = to spend time on something intentionally

In this sentence, the focus is on the situation itself:

• 返事に時間がかかっています
• The reply is taking time

That sounds neutral and descriptive.

If you said:

• 返事に時間をかけています

it would sound more like:

• someone is deliberately spending time on the reply

That is a different nuance. Here, かかっています is better because it describes a delay or time requirement, not a deliberate effort.

Here, -ている shows an ongoing current state.

• 時間がかかる = it takes time
• 時間がかかっています = it is taking time / it has been taking time

The idea is that the delay is happening right now.

So the sentence is not just a general statement like:

• Replies take time

It is saying:

• At the moment, the reply is taking time

This makes sense because the speaker is explaining the present situation.

The first part gives the apparent reason, and the second part gives the result.

• 担当部署がまだ決まっていないらしくて = apparently the responsible department hasn’t been decided yet
• 返事に時間がかかっています = so the reply is taking time

So the flow is:

1. the department in charge has apparently not been decided yet
2. because of that, the reply is delayed

The て in らしくて links the clauses in a way that often suggests and so or because of that.

That’s normal in Japanese. The sentence leaves the agent unstated because it is either obvious from context or not important.

What matters here is the situation:

• the responsible department is not yet decided
• therefore the reply is taking time

The sentence does not explicitly say who is delaying the reply. Depending on context, it could be:

• a company
• an office
• a team
• the person being contacted

Japanese often omits subjects and agents when they can be understood from context.

The comma helps readability, but it is not essential grammar.

It shows a pause between:

• the explanation
• the result

So it makes the sentence easier to process:

• 担当部署がまだ決まっていないらしくて、
• 返事に時間がかかっています。

In writing, Japanese commas are often used more flexibly than English commas. This one is natural, but the sentence could still be understood without it.

It is understandable and fairly natural, but by itself it is more like a neutral explanatory statement than very formal business wording.

A more polished business-style version might be something like:

• 担当部署がまだ決まっていないようで、ご返答までにお時間をいただいております。

That said, your original sentence is perfectly useful for learning because it clearly shows several common patterns:

• まだ ～ていない
• らしい / らしくて
• ～に時間がかかる
• ～ています for an ongoing situation