Learn Hardcore Russian: Моя жена сегодня работает дома.

жена (wife) is a feminine noun.
The feminine form of my is моя.
The masculine form мой is used with masculine nouns (e.g. мой брат – my brother).

So you get:

моя жена – my wife
мой муж – my husband
моё окно – my window (neuter)
мои дети – my children (plural)

What tense/aspect is работает, and why does it translate as “is working”?

Работает is:

present tense
3rd person singular
from the imperfective verb работать (to work)

Russian does not have a special progressive form like English “is working.” The simple present of an imperfective verb usually covers both:

Она работает. – She works. / She is working.

Context (like сегодня – today) tells us that here it is about what is happening today, so we naturally translate:

Моя жена сегодня работает дома. – My wife is working at home today.

What is the role of сегодня in the sentence, and where can it go?

Сегодня means today. It’s a time adverb and is quite flexible in position. All of these are correct and natural, with slightly different emphasis:

Моя жена сегодня работает дома. (neutral, very common)
Сегодня моя жена работает дома. (slight emphasis on “today”)
Моя жена работает сегодня дома. (small emphasis on “at home today”, not on other days)

Basic rule: time adverbs like сегодня, вчера, завтра often come:

at the beginning of the sentence, or
right before the verb.

What does дома mean exactly, and why is there no separate word for “at”?

Дома here means “at home”. It already includes the idea of “at”; you don’t need a separate preposition.

Compare:

дома – at home (location)
Я дома. – I am at home.

English needs a preposition (at home), but Russian often uses special adverb-like forms (like дома) without a preposition. So работает дома literally is “works home,” but idiomatically “works at home.”

What’s the difference between дома, домой, and в доме?

They all relate to дом (house, home) but express different things:

дома – at home (location)
- Она сегодня работает дома. – She is working at home today.
домой – (to) home (direction, movement towards home)
- Она идёт домой. – She is going home.
в доме – in the house (inside the building, more literal)
- Она работает в доме. – She works in the house (in that building),
  not necessarily “working from home” in the modern sense.

In your sentence, дома is used because the idea is “working at home” (not at the office, etc.).

What cases are used in Моя жена сегодня работает дома?

Word by word:

Моя жена – жена is in the nominative (subject of the sentence).
- моя is also nominative feminine singular, agreeing with жена.
сегодня – an adverb (no case).
работает – verb; verbs don’t have case.
дома – historically a case form (genitive/locative of дом),
but in modern Russian it is usually treated as an adverb meaning “at home.”

So the only clear case-marked noun here is жена in the nominative as the subject.

Can I leave out моя and just say Жена сегодня работает дома?

Yes, Жена сегодня работает дома is grammatically correct, but the nuance changes:

Моя жена сегодня работает дома. – clear: my wife.
Жена сегодня работает дома. – literally “(The) wife is working at home today.”

Without моя, it can sound like:

casual/familiar speech where it’s already obvious we’re talking about my wife, similar to English “The wife is working at home today,” or
a generic statement about some wife in a very specific context (less common).

For learners, it’s safer to include моя when you mean my wife, unless the context is absolutely clear.

Could I say Она сегодня работает дома instead of Моя жена…?

Yes:

Она сегодня работает дома. – She is working at home today.

Use она (she) when:

you have already mentioned моя жена earlier, or
it’s obvious from context who you are talking about.

Russian often avoids repeating full noun phrases and switches to pronouns once the person has been introduced.

How do I change this sentence to past or future?

Base sentence (present):

Моя жена сегодня работает дома. – My wife is working at home today.

Past (yesterday):

Моя жена вчера работала дома. – My wife was working / worked at home yesterday.

Changes:

сегодня → вчера (today → yesterday)
работает → работала (past tense, feminine, singular)

Future (tomorrow):

Моя жена завтра будет работать дома. – My wife will be working at home tomorrow.

Changes:

сегодня → завтра (today → tomorrow)
работает → будет работать (future with auxiliary будет
- infinitive)

Russian often uses будет + infinitive for the future of imperfective verbs.

How do I make this sentence negative or turn it into a yes–no question?

Negative:

Моя жена сегодня не работает дома.
– My wife is not working at home today.

You just put не directly before the verb работает.

Yes–no question (spoken):
Usually just change the intonation; the word order often stays the same:

Моя жена сегодня работает дома? – Is my wife working at home today?

You can also add the particle ли for a more formal or careful style:

Моя жена сегодня работает ли дома? – grammatically possible but sounds unusual here; more natural:
- Моя ли жена сегодня работает дома? (emphasis on my wife).

For everyday speech, simply raising your voice at the end is enough:
Моя жена сегодня работает дома?

How do I pronounce this sentence, and where is the stress?

Stresses (marked with an accent):

Моя́ жена́ сего́дня рабо́тает до́ма.

Syllable stresses:

мо-Я́
же-НА́
се-ВО́-дня (the -дн- cluster is pronounced almost like -дн’а)
ра-БО́-та-ет
ДО́-ма

Approximate phonetic reading (English-style):

ma-YA zhee-NA see-VOHD-nya ra-BO-ta-yet DO-ma

This will be understood and is a good starting point for pronunciation practice.