haha ga bangohan wo tukutte iru aida, watasi ha daidokoro de araimono wo simasu.

This is a very common question.

• が in 母が marks the subject of the clause 晩ご飯を作っている.
  • It tells us who is making dinner.
• は in 私は marks the topic of the main clause.
  • It tells us that the sentence is now talking about what I do.

So the sentence has two parts:

• 母が晩ご飯を作っているあいだ = while my mother is making dinner
• 私は台所で洗い物をします = as for me, I do the dishes in the kitchen

Using が for 母 and は for 私 is very natural here because the sentence contrasts two people’s actions:

• Mother is making dinner
• I am doing the dishes

作っている is the ている form of 作る.

• 作る = to make
• 作っている = is making / making

In this sentence, it describes an action that is in progress:

• 母が晩ご飯を作っている = my mother is making dinner

So here, ている works like the English progressive is making.

あいだ（間） means while or during.

It attaches to the phrase before it, so:

• 母が晩ご飯を作っているあいだ = while my mother is making dinner

The idea is:

• action/state before あいだ = the time period
• main clause after it = what happens during that time

So the sentence structure is basically:

• [while X is happening], Y happens

Here:

• X = mother is making dinner
• Y = I do the dishes

Because 作っているあいだ emphasizes the time while the action is ongoing.

• 作るあいだ would sound more like during the time of making in a more general or less natural way here
• 作っているあいだ clearly means while she is in the middle of making dinner

For actions in progress, V-ている あいだ is very common.

So:

• 勉強しているあいだ = while studying
• 寝ているあいだ = while sleeping
• 作っているあいだ = while making

Both are possible, but they give slightly different impressions.

• 洗い物をします = I do the dishes
• 洗い物をしています = I am doing the dishes

In Japanese, the non-past form します can describe:

• a habitual action
• a general statement
• something that happens in that situation

So this sentence can mean something like:

• While my mother is making dinner, I do the dishes as a routine or general pattern.

If you want to strongly emphasize that it is happening right now, you could say:

• 母が晩ご飯を作っているあいだ、私は台所で洗い物をしています。

That would sound more explicitly like:

• While my mother is making dinner, I am doing the dishes.

洗い物 literally means things to wash, but in everyday Japanese it often means:

• the dishes
• dishwashing
• washing up

So in this sentence:

• 洗い物をします = do the dishes

It does not only refer to plates specifically; it can include cups, utensils, cookware, and so on.

Because 洗い物 is the object of します in this expression.

• 洗い物をする is a fixed, very common expression meaning to do the washing / do the dishes

So:

• を marks what is being done

Other similar expressions:

• 勉強をする = to study
• 掃除をする = to clean
• 洗濯をする = to do laundry

Even though English says do the dishes, Japanese uses 洗い物をする as a standard verb phrase.

で marks the place where an action happens.

So:

• 台所で = in the kitchen
• literally, at/in the kitchen, as the place where the action is done

Compare:

• 台所で洗い物をします = I do the dishes in the kitchen
• 学校で勉強します = I study at school

So here, で tells us the location of the action します.

Yes, very naturally.

Japanese often omits words if they are clear from context. So this sentence could become:

• 母が晩ご飯を作っているあいだ、台所で洗い物をします。

That can still mean:

• While my mother is making dinner, I do the dishes in the kitchen.

However, 私は is useful if you want to:

• make the subject clear
• emphasize contrast with 母
• sound a little more explicit for learners

So both are fine.

Yes, but the nuance changes.

• 母 is the humble/plain way to refer to my mother when talking to other people
• お母さん is what you often say when addressing your mother, or when referring to someone else’s mother, or sometimes in casual family speech

In a neutral sentence like this, 母 is very natural if the speaker is talking about their own mother.

So:

• 母が晩ご飯を作っているあいだ… = natural when talking about your own mother

Using お母さん is not impossible, but 母 is the standard form in this kind of sentence.

They are all related and can often be translated as dinner.

• 晩ご飯（ばんごはん） = dinner, evening meal; casual and common
• 夕飯（ゆうはん） = dinner, supper; also common and casual
• 夕食（ゆうしょく） = evening meal; a bit more formal

In this sentence, 晩ご飯 sounds very natural and everyday.

The structure is:

• 母が = my mother
• 晩ご飯を = dinner
• 作っている = is making
• あいだ = while
• 私は = as for me
• 台所で = in the kitchen
• 洗い物をします = do the dishes

So the pattern is:

• [Person A が action-ている あいだ]、[Person B は place で action する]

This is a very useful pattern for making sentences with while.

For example:

• 父が新聞を読んでいるあいだ、私は宿題をします。
  • While my father is reading the newspaper, I do my homework.

This is an excellent grammar question.

• あいだ focuses on an action continuing throughout that time
• あいだに often focuses on something happening at some point within that time

In your sentence:

• 母が晩ご飯を作っているあいだ、私は洗い物をします suggests that my dishwashing happens during the whole period, or generally while she is cooking.

If you said:

• 母が晩ご飯を作っているあいだに、私は洗い物をします it can sound more like:
• At some point while my mother is making dinner, I do the dishes

So あいだ is the better choice when two actions overlap as ongoing activities.

Yes, to some extent.

Japanese word order is more flexible than English, as long as the particles stay correct. For example, these are all understandable:

• 母が晩ご飯を作っているあいだ、私は台所で洗い物をします。
• 私は、母が晩ご飯を作っているあいだ、台所で洗い物をします。
• 母が晩ご飯を作っているあいだ、台所で私は洗い物をします。

However, the original version is the most natural and easiest for learners:

• time clause first
• main clause second

So yes, the order can shift, but the original sentence is a very good standard pattern.