Learn Hardcore Chinese: lǎoshī shuō wǒmen děi hǎohāo zuò zhèxiē liànxí. - The teacher said we must do these exercises carefully.

说得很好 – speak very well (here 得 de links the verb 说 to the complement 很好)
慢慢地走 – walk slowly (here 地 de links an adverb to a verb)
我的书 – my book (here 的 de links a modifier to a noun)

So:

得 (děi) in this sentence = a separate word meaning must / have to.
得 (de), 的 (de), 地 (de) = unstressed particles that link parts of the sentence.

They are different in meaning, position, and pronunciation (děi vs de).

How strong is 得 (děi)? Does it mean must, have to, or should? How is it different from 要 (yào), 应该 (yīnggāi), and 必须 (bìxū)?

In everyday Mandarin, 得 (děi) is quite strong. It usually corresponds to must / have to rather than just should.

我们得好好做这些练习。
→ We have to / must do these exercises properly.
(sounds like a real requirement, probably from the teacher or the course)

Comparison:

要 (yào)
- Can mean want to, going to, or have to, depending on context.
- 我们要好好做这些练习。 – could feel a bit more neutral; obligation but slightly softer or more general.
应该 (yīnggāi)
- Means should / ought to (advice, expectation, not absolute obligation).
- 我们应该好好做这些练习。 – We should do these exercises properly.
必须 (bìxū)
- Very strong and formal: must, absolutely have to.
- 我们必须好好做这些练习。 – We must do these exercises (no choice).

Very rough strength scale (from weaker to stronger in obligation):

应该 ≲ 要 < 得 (děi) ≲ 必须

What exactly does 好好 (hǎohāo) mean here? Does it mean well, carefully, or something else?

好好 (hǎohāo) is a reduplicated form of 好 (hǎo, good) and here it functions like an adverb. It roughly means:

properly
carefully
seriously
thoroughly

In this sentence:

好好做这些练习
→ do these exercises properly / seriously / carefully

Nuances:

It is colloquial and common.
Often used by teachers, parents, bosses, etc. when telling someone to put in real effort, not just go through the motions.

Examples:

你得好好学习。 – You have to study properly / really study.
好好休息。 – Rest well / really get some good rest.

So it is more than just do them well; it carries a feeling of take this seriously and put effort into it.

Why is there no 地 (de) after 好好? Can I also say 好好地做这些练习?

Both:

好好做这些练习
好好地做这些练习

are grammatically correct.

Why no 地 is needed:

好好 is a very common, almost fixed, colloquial pattern used directly before a verb:
- 好好学习 – study properly
- 好好想一想 – think carefully
- 好好休息 – rest well
In modern spoken Mandarin, many short, common adverb-like words (especially reduplicated ones) can appear without 地.

The version 好好地做这些练习:

Sounds a bit more formal or careful, and
Emphasizes the manner slightly more explicitly.

In everyday conversation, 好好做这些练习 is more natural and more frequent.

Why is the order 好好做这些练习 instead of 做这些练习好好, like English do these exercises well?

Chinese and English place manner words differently.

In Chinese, adverbs like 好好, 认真, 仔细 usually go before the verb:

我们得好好做这些练习。
→ literally: we must properly do these exercises.

Basic structure here is:

老师 (subject 1) + 说 (verb 1) +
我们 (subject 2) + 得 (modal) + 好好 (adverb) + 做 (verb 2) + 这些练习 (object)

If you put 好好 after the object:

✗ 我们得做这些练习好好 – not correct in this simple form.

To put something like well at the end in Chinese, you usually need a result or degree complement with 得 (de):

我们得把这些练习做得很好。 – We must do these exercises very well.
这些练习要做得很认真。 – These exercises must be done very seriously.

So:

Adverb before verb → 好好做这些练习
Result complement after verb → 做得很好 / 做得很认真, but with a different structure.

Why do we use 做 (zuò) with 练习 (liànxí)? Could we just say 练习这些 or only 练习?

Here 练习 (liànxí) is used as a noun, meaning exercises (for example, exercises in a workbook). When referring to specific written exercises or tasks, Chinese commonly uses 做 (zuò, to do):

做作业 – do homework
做题 – do questions / problems
做练习 – do exercises

So:

做这些练习 → do these exercises

If you say 练习 as a verb, it usually means to practice [a skill], not to do specific written exercises:

练习说中文 – practice speaking Chinese
练习写字 – practice writing characters
多练习 – practice more

练习这些 by itself is odd because 这些 needs a clear noun after it. You could say:

练习这些语法点。 – practice these grammar points.

But for workbook-style exercises, 做练习 / 做这些练习 is the standard expression.

Is a measure word missing between 这些 and 练习? Should it be 这些个练习 or something like that?

Nothing is missing; 这些练习 is perfectly normal.

Reason 1:
些 (xiē) itself functions like a kind of measure word / quantifier meaning some / several. The pattern is:

这 + 些 + noun

So 这些练习 ≈ these exercises. You do not need an extra 个 here.

Reason 2:
For some nouns, especially those that are task- or activity-like, 这 / 那 / 一些 / 这些 can go directly before the noun:

这些作业 – this homework / these assignments
那些问题 – those questions
这些练习 – these exercises

If you want to emphasize counting them individually, you can add a more specific classifier, for example:

这几道练习题 – these several exercise questions
(here 道 is a common classifier for exam questions / problems)

But in the original sentence 这些练习 is simple and natural, and you do not say 这些个练习 in standard Mandarin.

Does 我们 include the teacher or only the students here? Could we leave 我们 out of the sentence?

Grammatically, 我们 (wǒmen) just means we / us; whether it includes the teacher depends on context and speaker.

In your sentence:

老师说我们得好好做这些练习。

There are two likely situations:

You are telling someone what the teacher said:
- Then 我们 usually means we students (the group that the teacher is talking to).
The teacher is speaking and uses 我们:
- Teachers sometimes say 我们要好好学习 meaning we (teacher + students) must study hard, as a polite or inclusive way to refer mainly to the students.

You cannot tell just from the grammar whether the teacher is included; context decides.

As for leaving 我们 out:

老师说，要好好做这些练习。 – literally: The teacher said (that one / people) should do these exercises properly.
- Here the subject is understood from context (probably you students).

But:

老师说我们得好好做这些练习。
makes it clear that the group referred to is 我们, not some other people.

You generally would not say:

✗ 老师说得好好做这些练习。

Because that looks like 说得 (say + 得 particle), which is a different structure and becomes confusing.

Is 老师说我们得好好做这些练习 direct speech or reported speech? Where would commas or quotation marks go in written Chinese?

As written, 老师说我们得好好做这些练习 is most naturally understood as reported (indirect) speech:

The teacher said that we must do these exercises properly.

If you want to write direct speech, you normally show it with punctuation:

Colon and quotation marks:
- 老师说：“我们得好好做这些练习。”
  → The teacher said: We must do these exercises properly.
Comma before the quote is also common in less formal writing:
- 老师说， “我们得好好做这些练习。”

In spoken Chinese, both direct and indirect versions can sound very similar. Context and intonation tell you which it is. The version without punctuation markers (no colon, no quotes) is usually taken as indirect:

老师说我们得好好做这些练习。
→ The teacher said we must do these exercises properly.

How is the whole sentence pronounced naturally? Are there any tone changes (tone sandhi)?

The basic pinyin with tones is:

老师说我们得好好做这些练习。
lǎoshī shuō wǒmen děi hǎohāo zuò zhèxiē liànxí

In natural speech, some tone sandhi (tone changes) happen:

老 (lǎo, 3rd tone) + 师 (shī, 1st tone)
- A 3rd tone before a non-3rd tone is often pronounced as a half-3rd, sounding closer to a low dipping tone:
- So 老 is not fully pronounced as a long falling-rising; it is shortened.
得 (děi, 3rd) + 好 (hǎo, 3rd) in 得好好
- When a 3rd tone is followed by another 3rd tone, the first one changes to 2nd tone in pronunciation.
- So 得好好 is pronounced like: dé háohāo (but still written děi hǎohāo in pinyin with tone marks).

Putting it together, very roughly (marking how it sounds, not official tone marks):

lǎo shī shuō wó men dé háo hāo zuò zhè xiē liàn xí

But in writing you keep the dictionary tones:

老师 (lǎoshī)
说 (shuō)
我们 (wǒmen)
得 (děi)
好好 (hǎohāo)
做 (zuò)
这些 (zhèxiē)
练习 (liànxí)

Just remember that 3rd + 3rd becomes 2nd + 3rd in actual pronunciation.