haha ha tumetai touhu ni syouyu wo kakete, watasi ni dasimasu.

は marks 母 as the topic: As for my mother, ...

So the sentence is presenting what the mother does. In many beginner sentences, は is used this way to set the scene.

If you used 母が, it would put more focus on mother as the subject, as if answering Who does this?
For example:

• 母は冷たい豆腐にしょうゆをかけて、私に出します。
  As for my mother, she puts soy sauce on cold tofu and serves it to me.
• 母が冷たい豆腐にしょうゆをかけて、私に出します。
  My mother is the one who puts soy sauce on it and serves it to me.

Both can be grammatical, but は is the more neutral choice here.

Yes, here 母 normally means my mother.

In Japanese, when talking about your own mother to someone else, you often use:

• 母（はは） = my mother

But when addressing your mother directly, or when referring to someone else’s mother politely, you often use:

• お母さん（おかあさん）

So:

• 母は... = My mother...
• お母さん、これ見て。 = Mom, look at this.

This is a common social nuance in Japanese.

Because Japanese adjectives come before the noun they modify.

• 冷たい豆腐 = cold tofu

This works much like English in this case:

• cold tofu
• small dog
• interesting book

Also, 冷たい is an -i adjective, so it can directly modify a noun with no extra word:

• 冷たい水 = cold water
• 熱いお茶 = hot tea
• 古い本 = old book

With the verb かける in this meaning (to pour/sprinkle something onto something), the thing receiving the action is often marked with に.

So:

• 豆腐に = onto the tofu
• しょうゆを = soy sauce
• かけて = pouring/putting on

So the structure is:

• [target] に [thing being poured] を かける

Examples:

• ご飯にふりかけをかける = put furikake on rice
• サラダにドレッシングをかける = pour dressing on a salad
• 豆腐にしょうゆをかける = pour soy sauce on tofu

Because しょうゆ is the direct object of かける.

In other words, the soy sauce is the thing being applied or poured.

• 豆腐に = onto the tofu
• しょうゆを = soy sauce
• かける = to pour/apply

So を marks what is being poured, while に marks where it goes.

かけて is the -て form of かけます.

Here, the -て form connects two actions:

1. しょうゆをかけて = pour soy sauce on it
2. 私に出します = serve it to me

So the whole sentence means something like:

• My mother pours soy sauce on cold tofu and serves it to me.

In this use, the -て form often means:

• and
• then
• after doing that

It links actions in sequence.

This に marks the recipient of the action 出します.

• 私に出します = serves it to me

So there are two different に particles in the sentence, doing two different jobs:

• 豆腐に = onto the tofu
• 私に = to me

This is very normal in Japanese. The same particle can have different related functions depending on the verb.

Good question. 出す has several meanings depending on context.

Common meanings include:

• to take out / bring out
• to send / submit
• to serve / put out (food)

Here, because the sentence is about tofu and soy sauce, 出します means:

• serve
• set out
• put in front of someone

So 私に出します means:

• she serves it to me
• she puts it out for me

This is a very natural use of 出す with food.

Because Japanese often leaves out things that are already understood from context.

The sentence first mentions:

• 冷たい豆腐にしょうゆをかけて = puts soy sauce on the cold tofu

Then:

• 私に出します = serves it to me

The object of 出します is omitted because it is obvious that the thing being served is the tofu.

In English, we usually repeat it:

• ...and serves it to me.

In Japanese, leaving it out sounds natural.

Yes. The sentence suggests this order:

1. The mother puts soy sauce on the cold tofu.
2. Then she serves it to me.

Because the first verb is in the -て form, it usually shows that the first action happens before the second one, or at least that they are connected in that order.

So this does not just list random actions. It presents a sequence.

Literally, it means cold tofu. But in Japanese, this often brings to mind a common dish: chilled tofu, often called 冷ややっこ（ひややっこ）.

That said, in this sentence, you only need to understand it as:

• cold tofu
• probably tofu served chilled, often with soy sauce

So there may be a cultural association, but grammatically it is simply cold + tofu.

Yes. A few natural translations are:

• My mother pours soy sauce on cold tofu and serves it to me.
• My mother puts soy sauce on cold tofu and serves it to me.
• My mother pours soy sauce over the cold tofu and serves it to me.

The exact English wording can vary, especially for:

• かける → pour / put on / pour over
• 出す → serve / set out

But the basic meaning stays the same.