Learn Hardcore Japanese: mazu tumetai mizu to atui otya wo youisite, sorede yukkuri hanasou. - First prepare cold water and hot tea, and then let’s talk at ease.

まず means "first (of all)/to begin with." It's a sentence adverb placed at the start to order steps. It doesn't take a particle. Close alternatives: まずは (slightly softer), 最初に (more literal "at first").

Why is there only one を after 冷たい水と熱いお茶?

In Japanese, when you list nouns with と ("and"), you attach the case particle once to the whole list: AとBをV. Repeating を after each item is ungrammatical.

What's the difference between 冷たい/寒い and 熱い/暑い?

冷たい: cold to the touch; also "cold" in attitude. Used for objects/liquids like 冷たい水.
寒い: cold air/temperature of the environment or how you feel physically.
熱い: hot to the touch; for objects/liquids like 熱いお茶.
暑い: hot weather/air temperature.

How do you pronounce each word (including を)?

まず (mazu), つめたい (tsumetai), みず (mizu), あつい (atsui), おちゃ (ocha), を (o), よういして (yōi shite), それで (sore de), ゆっくり (yukkuri), はなそう (hanasō). In modern Japanese, the particle を is pronounced "o".

Why use the て-form (用意して) here? How is it different from 用意してから?

用意して links actions: "prepare ... and (then) ...". The time order is understood from context.
用意してから explicitly means "after preparing (completely), then ...". It emphasizes finishing the first action before starting the next. Both are fine here; 〜てから is a bit more explicit.

What does それで mean here? How is it different from それから or そして?

それで: "so; and then; with that (as a result/next step)". It often signals that the next action follows naturally from the previous one.
それから: "after that" (pure sequence in time).
そして: "and" (just adds information; weaker sense of sequence). In this sentence, all three can work. If you want a neutral "after that," それから is the safest. それで adds a light "so/with that settled" feeling.

Is それで necessary? Can I just say 用意して、ゆっくり話そう?

Yes, you can drop it. 用意して、ゆっくり話そう is natural. Alternatives:

用意してから、ゆっくり話そう (clearer "after that")
用意して。それから、ゆっくり話そう。 (two sentences)

What does 話そう express? How is it different from 話しましょう?

話そう is the plain volitional form: an inclusive suggestion "let's talk." It's casual. The polite counterpart is 話しましょう. Other casual invitations: 話さない？ (Wanna talk?), 話そうか (Shall we talk?).

Does ゆっくり need と (as in ゆっくりと)? What's the nuance?

ゆっくり by itself is already an adverb meaning "slowly/at leisure/calmly." ゆっくりと is a bit more formal or emphatic. In everyday speech, ゆっくり話そう is the default.

Why is there no subject like "we"? Who is doing the actions?

Japanese often omits subjects when obvious from context. With a volitional like 話そう, the default subject is the speaker plus the listener ("let's ..."), so "we" is implied.

What's the nuance difference between 用意する, 準備する, and お茶を入れる?

用意する: prepare/get ready tangible things (drinks, documents, seats). Fits well here.
準備する: broader "prepare" (plans, studying, equipment). Also acceptable but slightly more general.
お茶を入れる: specifically "brew/make tea." If you want to emphasize brewing, say 熱いお茶を入れて.

Can I say 冷たいお茶 or 熱い水?

冷たいお茶 is common ("cold/chilled tea").
熱い水 is uncommon; for "hot water" people say お湯 (or 熱湯 for "boiling water"). 冷たい水 is the natural way to say "cold water."

Why use と between the drinks? Could I use や or とか?

AとB: exhaustive "A and B (just those)".
AやB: non-exhaustive "A, B, and the like."
AとかB: casual, also non-exhaustive. All take the particle after the whole list: AやBを用意して.

Is the で in それで the same as the particle で?

Historically it's それ + で, but in use それで functions as a fixed connective meaning "so/and then." It's not the locative/instrumental particle で inside your clause.

Why are there spaces in the sentence? Are they standard?

Ordinary Japanese writing doesn't put spaces between words. Textbooks add spaces to help learners. A natural punctuation-only version is: まず、冷たい水と熱いお茶を用意して、それでゆっくり話そう。

How would I make the whole sentence polite?

Use the polite volitional or -ます forms:

まず、冷たい水と熱いお茶を用意して、それからゆっくり話しましょう。 If you, as the speaker, will prepare them for the listener (service nuance), you can say:
まず、冷たい水と熱いお茶をご用意しますので、そのあとでゆっくりお話ししましょう。