Learn Hardcore Czech: Dnes jsou všichni doma.

všichni = they (all) → jsou (are)
English everyone is grammatically singular, but Czech uses a plural subject and therefore a plural verb.

So:

Dnes jsou všichni doma. = Today all (of them) are at home. → idiomatic English: Today everyone is at home.

What is the difference between všichni and každý, since both can translate as everyone?

Both can correspond to everyone, but they focus on different things:

všichni = all (people) as a group (plural)
- Všichni jsou doma. – All of them are at home.
každý = each / every (person) individually (singular)
- Každý je doma. – Each person is at home.

In meaning, Všichni jsou doma. and Každý je doma. end up describing the same situation, but:

všichni emphasizes the group as a whole.
každý emphasizes every individual member.

In your sentence, všichni is the more natural, neutral choice for everyone.

Why isn’t there a pronoun like oni (they) in the sentence?

Czech is a pro‑drop language: subject pronouns are usually omitted when the verb ending already shows the person and number.

Oni jsou doma. – They are at home.
Jsou doma. – (They) are at home.

Because jsou is clearly 3rd person plural, and we also have všichni, there is no need to say oni.
Dnes jsou všichni doma. is the normal, natural way to say it.

What case is všichni, and what is its base (dictionary) form?

Všichni is nominative plural (subject of the sentence).
The dictionary form is všechen (meaning all / every).

Rough paradigm (masculine animate, singular → plural):

singular: všechen (all, every)
plural nominative: všichni (all [people])

So in this sentence všichni behaves like they all as the subject.

Could the word order be Všichni jsou dnes doma instead of Dnes jsou všichni doma? Is there a difference?

Yes, you can say both:

Dnes jsou všichni doma.
Všichni jsou dnes doma.

Both are correct and both can mean Today everyone is at home.

Nuance (very fine and context‑dependent):

Dnes jsou všichni doma. – slight emphasis on today as the time frame (e.g. compared to other days).
Všichni jsou dnes doma. – slight emphasis on everyone (e.g. compared to only some people being home).

In everyday speech, both are very natural and often interchangeable.

Is Dnes required? Could I say only Všichni jsou doma?

You can absolutely say:

Všichni jsou doma. – Everyone is at home.

Adding dnes just specifies when.
So:

Všichni jsou doma. – general/current situation (no specified time, could be now).
Dnes jsou všichni doma. – specifically today.

What part of speech is doma? Why not v domě or v domu?

Doma is an adverb meaning at home. It is not declined; it has no case.

doma = at home (general place where someone lives)
v domě / v domu = in the house / in a house (more concrete, literally inside a building)

In this sentence, we are talking about being at home in the usual sense (their place of residence), so doma is the natural word.

What is the difference between doma, domů, and domov?

These are related but different:

doma – adverb of location: at home
- Jsou doma. – They are at home.
domů – adverb of direction: (to) home
- Jdou domů. – They are going home.
domov – noun: home (as a place or concept)
- Mám rád svůj domov. – I love my home.

Your sentence uses a location (where they are), so it needs doma, not domů.

If the group consists only of women, do we still say všichni?

For a group of only women, the grammatically correct form is:

Dnes jsou všechny doma. – Today they are all at home. (all women)

However, in mixed groups or when gender is not specified, Czech uses the masculine animate plural as the default generic:

Dnes jsou všichni doma. – Today everyone (men + women, or gender‑mixed) is at home.

So:

Only women: všechny.
Mixed or unknown gender: všichni (default and most common in general statements).

What is the difference between všichni and všechno?

všichni – all (people), everyone (masculine animate plural)
- Všichni jsou doma. – Everyone is at home.
všechno – everything (neuter singular, non‑persons, things/abstracts)
- Všechno je doma. – Everything is at home. (e.g. all your stuff has arrived)

So use:

všichni for people.
všechno for things or abstract stuff.

Can we leave out the verb jsou, like in Russian where you can say just Сегодня все дома?

No. In standard Czech, the verb být (to be) is not usually omitted in the present tense.

You must say:

Dnes jsou všichni doma. – with jsou.

Saying Dnes všichni doma (without jsou) sounds incomplete or incorrect in standard Czech. The verb jsou is required here.

How do I say Everyone will be at home today or Everyone was at home?

You keep všichni doma, and just change the verb být:

Present: Dnes jsou všichni doma. – Today everyone is at home.
Future: Dnes budou všichni doma. – Today everyone will be at home.
Past: Včera byli všichni doma. – Yesterday everyone was at home.

So:

jsou – are (present)
budou – will be (future)
byli – were (past, masculine/mixed group generic)

Is Všichni doma dnes jsou possible, or putting dnes at the very end like Všichni jsou doma dnes?

Všichni jsou doma dnes. – Grammatically possible, but sounds a bit marked or less natural; dnes is rarely placed at the very end in neutral speech.
Všichni doma dnes jsou. – Very unusual and sounds awkward or poetic; not normal everyday Czech.

For neutral, natural word order, use:

Dnes jsou všichni doma.
or
Všichni jsou dnes doma.