tā xiào zhe shuō, zài jiā yìzhí wán yóuxì de shíhou, chángcháng huì wàngjì shíjiān; zài gōngyuán dǎ lánqiú búdàn duì jiànkāng hǎo, érqiě kěyǐ tígāo xìnxīn.

着 here shows a continuing accompanying action.
So 笑着说 means speaking while smiling.

A helpful way to think about it:

• 笑 = smile / laugh
• 说 = speak
• 笑着说 = say something with a smile, or while smiling

Why not 笑地说?

• 地 is often used when an adjective or descriptive phrase modifies a verb, like 高兴地说 = say happily
• 笑 is an action verb, so 笑着说 is the natural pattern for doing one action while doing another

So this is a very common structure:

• 看着书听音乐 = listen to music while reading
• 站着说话 = speak while standing
• 笑着说 = say with a smile

Chinese often does not need a word like English that after verbs such as 说, 觉得, 知道, 想.

So:

• 她笑着说，...
  = She said, ...

The comma simply introduces what she said. Chinese often uses punctuation where English might use that or quotation marks.

You could also see other styles in writing, such as:

• 她笑着说：...
• 她笑着说： followed by direct speech

But 她笑着说，... is completely normal.

Not necessarily. This is a very common source of confusion.

Grammatically, the subject inside 在家一直玩游戏的时候 is not explicitly stated. So depending on context, it can mean:

• when she stays at home playing games all the time
• when someone stays at home playing games all the time
• when people stay at home playing games all the time

In this sentence, because it begins with 她笑着说, the whole thing is what she is saying, but the content itself can sound more like a general statement rather than a statement only about her.

If you wanted to make she clearly the subject of that clause, you could say:

• 她在家一直玩游戏的时候，常常会忘记时间。

If you wanted a general meaning, the original version works fine.

的时候 means when or at the time when.

It turns the phrase before it into a time expression:

• 在家一直玩游戏 = stay at home and keep playing games
• 在家一直玩游戏的时候 = when staying at home and continuously playing games

Then the main clause comes after it:

• 在家一直玩游戏的时候，常常会忘记时间。
• When ... , one often forgets the time.

This pattern is extremely common:

• 吃饭的时候 = when eating
• 上课的时候 = during class
• 下雨的时候 = when it rains

一直 often means continuously, all along, or without stopping for a stretch of time.

In this sentence:

• 在家一直玩游戏的时候
• not just playing games at home
• but keeping on playing games at home

It gives the feeling of sustained, uninterrupted activity.

It is not exactly the same as English always. Compare:

• 一直玩游戏 = keep playing games continuously
• 总是玩游戏 = always play games / play games all the time as a habit

So here 一直 focuses more on the activity continuing for a long period, which matches the next part:

• 常常会忘记时间 = often end up forgetting the time

They do different jobs.

• 一直 describes the manner/duration of the activity
  → continuously, without stopping
• 常常 describes the frequency of the result
  → often

So:

• 在家一直玩游戏的时候
  = when someone keeps playing games at home for a long time
• 常常会忘记时间
  = they often forget the time

In short:

• 一直 = continuous action
• 常常 = repeated frequency

Yes, 常常忘记时间 is already grammatical. Adding 会 changes the nuance slightly.

• 常常忘记时间 = often forget the time
• 常常会忘记时间 = often will / tend to forget the time

Here 会 does not mainly mean future tense. It often expresses:

• tendency
• likelihood
• what typically happens under certain conditions

So 常常会忘记时间 sounds like:

• when this happens, one often ends up forgetting the time
• it is easy to forget the time in that situation

This use of 会 is very common in Chinese.

Because this sentence is talking about a general tendency, not one completed event.

• 忘记时间 = forget the time, as a general action
• 忘记了时间 = forgot the time / have forgotten the time in a specific instance

In this sentence, the speaker is describing what often happens in that situation, so the plain verb form is more natural:

• 常常会忘记时间

If you said:

• 常常忘记了时间

that would sound less natural for a habitual statement.

This is mostly a vocabulary/collocation issue. In Chinese, different activities naturally pair with different verbs.

Common pairings:

• 玩游戏 = play games
• 打篮球 = play basketball
• 打网球 = play tennis
• 踢足球 = play soccer
• 下棋 = play chess

So English uses play for many things, but Chinese uses different verbs depending on the activity.

About 玩篮球:

• it is usually not the standard way to say play basketball
• it may sound like play around with a basketball rather than play the sport

So for the sport, 打篮球 is the correct natural expression.

Yes, in effect, the whole action phrase 在公园打篮球 functions like the subject/topic of the sentence.

Chinese often allows a verb phrase to act as the thing being discussed:

• 在公园打篮球不但对健康好，而且可以提高信心。

This means:

• Playing basketball in the park is not only good for health, but can also improve confidence.

So even though it looks like a verb phrase, it behaves like an English gerund phrase:

• Playing basketball in the park

This is very common in Chinese:

• 多喝水对身体好。
  Drinking more water is good for the body.
• 早睡早起很重要。
  Going to bed early and getting up early is important.

The pattern is:

• 对 + noun + 好
• = be good for + noun

So:

• 对健康好 = good for health

Examples:

• 对身体好 = good for the body
• 对孩子好 = good for children
• 对学习好 = good for studying

So in the sentence:

• 在公园打篮球不但对健康好，而且可以提高信心。

the first benefit is expressed with:

• 对健康好 = beneficial to health

A small note: in everyday speech, people may also say 对身体好 very often.

不但……而且…… means not only ... but also ...

In the sentence:

• 在公园打篮球不但对健康好，而且可以提高信心。

Structure:

• 不但 introduces the first point
  → 对健康好
• 而且 introduces the second point
  → 可以提高信心

So it means:

• playing basketball in the park is not only good for health, but also can improve confidence

This pattern is very common. For example:

• 他不但会说中文，而且会说日语。
  He can speak not only Chinese but also Japanese.

A useful note: the two parts after 不但 and 而且 should usually be reasonably parallel in meaning or structure.

信心 means confidence.
提高信心 means increase/improve confidence.

It is understandable and natural, but there is a nuance:

• 信心 = confidence in general, confidence about doing something
• 自信心 = self-confidence

So:

• 提高信心 = build up confidence
• 提高自信心 = improve self-confidence

In many contexts, both are possible, but 自信心 is a bit more specific.

Also, Chinese often uses 提高 with abstract things:

• 提高水平 = raise/improve one’s level
• 提高能力 = improve ability
• 提高效率 = improve efficiency

The semicolon separates two closely related but distinct statements inside the same stretch of speech.

The two parts are:

1. 在家一直玩游戏的时候，常常会忘记时间
2. 在公园打篮球不但对健康好，而且可以提高信心

These are related because both are part of what she is saying, but they are separate ideas:

• one about gaming at home
• one about playing basketball in the park

A comma might feel too weak because each part is already fairly long.
A period would also work in many contexts, but the semicolon nicely shows a close connection.

This is due to Mandarin tone change rules.

For 不:

• 不 is normally fourth tone: bù
• before another fourth-tone syllable, it changes to second tone: bú

Since 但 is fourth tone (dàn), we get:

• 不但 → búdàn

For 一:

• 一 changes tone depending on what follows
• before a fourth-tone syllable, it becomes second tone
• before a first, second, or third tone syllable, it becomes fourth tone

Since 直 is second tone (zhí), we get:

• 一直 → yìzhí

These tone changes are standard and very important for natural pronunciation.

Yes. The original sentence is grammatical, but for learners, a slightly more explicit version may be easier to read.

For example:

• 她笑着说，她在家一直玩游戏的时候，常常会忘记时间；在公园打篮球不但对健康好，而且还可以提高信心。

This version adds:

• another 她 to make the first clause’s subject clearer
• 还 before 可以 for a slightly fuller not only ... but also ... rhythm

But the original is still fine. Chinese often omits subjects when they are understood from context, and often prefers concise wording.