כשהילד התחיל לבכות, האחות שלו חייכה ונתנה לו מים.

Because כש־ is a prefix meaning when. Hebrew often attaches short function words directly to the following word, so כשהילד is really כש + הילד.

So:

• כש = when
• הילד = the boy / the child
• כשהילד = when the boy / child

A more formal equivalent would be כאשר הילד.

It can mean either boy or child depending on context, but in this sentence boy is the more natural translation. The feminine form is ילדה = girl.

So:

• ילד = boy / male child
• ילדה = girl / female child

Because the subject is הילד, which is masculine singular. In the past tense, Hebrew verbs agree with the subject in gender and number.

So:

• הילד התחיל = the boy started
• הילדה התחילה = the girl started

Because after התחיל = started, Hebrew normally uses an infinitive, just like English uses to + verb.

So:

• התחיל לבכות = started to cry

The ל־ at the beginning of לבכות is part of the infinitive form and often corresponds to English to.

That is a very common Hebrew way to show possession. Hebrew often says:

noun + possessive word

So:

• האחות שלו = his sister
• literally, something like the sister of him

The ה־ stays on אחות because the whole phrase is definite: you mean a specific sister, not just any sister.

Yes. אחותו also means his sister.

Both are correct, but they feel a little different:

• אחותו = more compact, often a bit more written or formal
• האחות שלו = very common in everyday speech

So this sentence could also be phrased with אחותו.

Because both verbs are in the feminine singular past tense, and their subject is האחות = the sister.

So:

• חייכה = she smiled
• נתנה = she gave

If the subject were masculine, you would get:

• חייך = he smiled
• נתן = he gave

The ו־ is the word and, and in Hebrew it is usually attached directly to the next word.

So:

• ו נתנה is written ונתנה
• חייכה ונתנה = smiled and gave

The subject does not need to be repeated because it is still the same person, האחות שלו. Hebrew does this just like English does in a sentence like his sister smiled and gave him water.

לו means to him.

It is made from:

• ל־ = to
• ו = him

With the verb נתן = gave, Hebrew usually marks the receiver with ל־:

• נתנה לו מים = she gave him water
• literally, she gave to him water

Because את is used before a definite direct object, and מים here is not marked as definite.

Compare:

• נתנה לו מים = she gave him water
• נתנה לו את המים = she gave him the water

So the absence of את tells you this is just water in a general sense, not the water.

Because מים is one of those Hebrew nouns that has a plural-looking form but is normally translated as a mass noun in English: water.

So even though it ends in ־ים, you usually translate it as singular in English. It is simply the normal Hebrew word for water.

Yes. אחות can mean either sister or nurse. Context tells you which one is meant.

In this sentence, if the meaning shown to the learner is his sister, then that is the intended reading. But in another context, האחות שלו could also mean his nurse.