Learn Hardcore Chinese: yīshēng shuō tā de shēntǐ bú tài hǎo, yào zài yīyuàn xiūxi. - The doctor said his health isn’t very good and that he needs to rest in the hospital.

By itself, 他 is ambiguous; it could be the patient or another male the doctor is talking about. The second clause 要在医院休息 shares the same (implicit) subject as that 他. To disambiguate:

If it’s the doctor himself: 医生说自己的身体不太好，要在医院休息。
If it’s a specific patient: 医生说小王的身体不太好，要在医院休息。
If it’s you: 医生说我的身体不太好，要在医院休息。

Why is 不太好 used? How is it different from 太不好, 很不好, and 不是很好?

不太好 = “not very good,” a mild, softer negative.
很不好 = “quite bad,” noticeably stronger than 不太好.
太不好了 = “way too bad/extremely bad” (dramatic; usually with 了).
太不 + adj. is common with disyllabic adjectives (e.g., 太不公平); 太不好 without 了 is uncommon in everyday speech.
不是很好 ≈ 不太好, but often sounds a touch more hedged. Positive counterpart: 他的身体很好 (“his health is very good,” with 很 as the usual linker).

What does 要 mean here—want to, will, or need to? Could I use 需要/得/必须/应该/会?

Here 要 expresses requirement/recommendation: “needs to/must.” Alternatives:

需要: need (objective necessity). 含义接近: 需要在医院休息.
得/必须: must (stronger obligation). 得在医院休息 / 必须在医院休息.
应该: should (advisory). 应该在医院休息.
会: will/likely to (not obligation). 会在医院休息 = “will rest in the hospital.”

Why is the place phrase before the verb (要在医院休息)? Can I say 休息在医院? What about 医院里?

Chinese places location before the action: [要] + 在 + 地点 + [休息]. So 要在医院休息 is natural; 休息在医院 is unnatural. You can add 里 to emphasize “inside”: 在医院里休息 (no big meaning change). Fronting for emphasis is also possible: 在医院，(他)要休息。

Why 他的身体 instead of 他身体? Can I drop 的? And is this 的 the same as 得/地?

With body parts and close relations, spoken Chinese often drops 的: 他身体不太好 (colloquial). 他的身体不太好 is equally correct and a bit more explicit/formal. Note:

的 marks possession/modification (e.g., 我的书).
得 marks complements of degree (e.g., 说得很好).
地 makes adverbs (e.g., 认真地学习).

Does 身体 mean “body” or “health”? How is it different from 健康 and 生病?

身体 in 身体不太好 means overall health/physical condition.
健康 is “health” (noun/adj.): 健康状况不太好 is formal; 很健康 = “very healthy.”
生病 is “to be/get sick” (an episode), e.g., 他生病了 (“he got sick”).

Why 说 and not 告诉? How do I include the person being told?

说 doesn’t require a listener: 医生说……
To name the listener: 对/跟 + 人 + 说 → 医生对我说…… / 医生跟我说……
告诉 requires a listener: 医生告诉我…… (you can’t say “医生告诉……” without an object).

Is 在医院休息 the same as 住院?

Not exactly.

在医院休息 = rest at the hospital (location emphasized; could be short-term).
住院 = be admitted/hospitalized. Doctors often say 要住院 or 需要住院观察. You can also say 要在医院休息几天/住院几天.

How do I add duration, like “rest for three days”?

Put the duration after the verb phrase:

要在医院休息三天/两周。 With 住院:
要住院一周。 For completed time: 他在医院休息了三天。

Where is the word “that” after 说? Is the comma okay? Can I use quotes?

Chinese doesn’t need a “that.” 说 + clause is standard. The comma links the two parts of what the doctor said. You can also write:

医生说：“他的身体不太好，要在医院休息。” If you want a logical connector: 医生说他的身体不太好，所以要在医院休息。

Do I need 了 after 说 to show past? What about 过?

Not required. Chinese often leaves tense to context.

医生说…… neutral; context supplies time.
医生说了…… emphasizes the completed act of saying.
医生说过…… = “has said (before).” Add time words for clarity: 昨天医生说……

Can 休息 take an object? Is “休息身体” okay?

休息 is intransitive; don’t attach an object like 身体. Natural patterns:

休息一下 / 休息一会儿 / 好好休息
在家/在医院休息
With duration: 休息三天

Any pronunciation tips in this sentence?

不 changes to second tone before a fourth tone: bú tài (不太).
休息 is pronounced xiūxi; the second syllable is often a neutral tone in speech.
医院 = yīyuàn, 医生 = yīshēng. The 医 here is not the number 一 (yī).
的 here is the neutral-tone particle de.

In speech, do 他 and 她 sound the same? How do I avoid confusion?

Yes—他/她/它 are all pronounced tā. Context usually clarifies. In writing, use the correct character. To avoid ambiguity, use the person’s name or add 自己 where appropriate (e.g., 医生说自己的身体……).