Learn Hardcore Czech: Dnes je moje dcera také unavená a chce spát. - Today my daughter is also tired and wants to sleep.

Because dcera (daughter) is a singular feminine noun in the nominative (it’s the subject), the adjective must also be feminine singular nominative → unavená.

If the subject were masculine or neuter, it would change:

Dnes je můj syn unavený. – Today my son is tired.
Dnes je to dítě unavené. – Today that child is tired.

Why is it moje dcera and not má dcera? Are both correct?

Both are correct; they’re just different forms of the same possessive.

For “my” (feminine singular) you can say:

moje dcera – more common in everyday speech
má dcera – shorter, a bit more formal / stylistic, often in writing or in more “elevated” style

Other examples:

moje máma / má máma – my mum
moje kniha / má kniha – my book

In normal spoken Czech, you will hear moje dcera much more often than má dcera.

Why does the adjective unavená come after the verb je? Could I say Dnes moje dcera unavená je?

The neutral word order in Czech is usually:

subject – verb – rest of the predicate
Moje dcera je unavená.

So Dnes je moje dcera unavená is very natural.

Czech word order is flexible, but Dnes moje dcera unavená je sounds very unusual and poetic or theatrical. You might see similar orders in poetry, songs, or to create strong emphasis, but in normal speech you keep:

Dnes je moje dcera unavená. (normal)
Dnes je unavená moje dcera. (emphasis on “my daughter”, not someone else)

What exactly does také mean here? Is it “also” or “too”? Who/what is she “also” with?

Také means also / too / as well, and it expresses addition. It doesn’t itself say what it is adding to; that comes from context.

Possible readings, depending on context:

Other people are tired:
Dnes jsem unavený a moje dcera je také unavená.
Today I’m tired and my daughter is tired too.
Or something else happened earlier and now, in addition, she is tired.

English has several options: also, too, as well. Také covers all of these; the sentence itself doesn’t say exactly what it is comparing to.

What’s the difference between také and taky?

They are near-synonyms:

také – a bit more formal, typical in writing, careful speech
taky – very common in everyday spoken Czech, more colloquial

Both mean also / too / as well.

So you can also say:

Dnes je moje dcera taky unavená a chce spát.
(perfectly natural in speech)

Can I move také to another place, like Dnes je také moje dcera unavená or Dnes je moje dcera unavená také?

Yes, but the focus shifts slightly:

Dnes je moje dcera také unavená.
Neutral: “My daughter is also tired today.”
Dnes je také moje dcera unavená.
Emphasis on moje dcera: “Today, my daughter too is tired” (maybe others have already been mentioned).
Dnes je moje dcera unavená také.
Sounds a bit marked/stylistic; can feel like you’re stressing unavená at the end:
“My daughter is tired today as well.”

All are grammatically possible, but the original sentence is the most neutral-sounding.

Why is it dcera and not dceru? Which case is this?

Dcera is in the nominative singular, because it’s the subject of the sentence.

Czech uses:

nominative for subjects:
Moje dcera je unavená. – My daughter is tired.
accusative for direct objects:
Znám svou dceru. – I know my daughter.
(here it’s dceru, accusative)

So:

Moje dcera je unavená. – nominative (subject)
Vidím svou dceru. – accusative (object)

Why is it chce spát and not chce spí?

After verbs like chtít (to want), Czech uses the infinitive of the second verb.

So you say:

chce spát – she wants to sleep
chci jíst – I want to eat
chtějí odjet – they want to leave

Spí is the finite present form (he/she/it sleeps / is sleeping), and you don’t use that directly after chce.

Compare:

Moje dcera spí. – My daughter is sleeping.
Moje dcera chce spát. – My daughter wants to sleep.

How is chtít (to want) conjugated? Why is it chce here?

Chce is the 3rd person singular present of chtít.

Present tense forms:

já – chci – I want
ty – chceš – you (sg) want
on/ona/ono – chce – he/she/it wants
my – chceme – we want
vy – chcete – you (pl/formal) want
oni – chtějí – they want

So:

Moje dcera chce spát. – My daughter wants to sleep.
Chci spát. – I want to sleep.
Děti chtějí spát. – The children want to sleep.

Could I say Dnes moje dcera je také unavená a chce spát instead? Is that okay?

Yes, it’s grammatically correct, but the most neutral word order in Czech is:

Dnes je moje dcera také unavená…

Placing je directly after dnes is very natural: time adverb → verb → subject.
Dnes moje dcera je také unavená… is understandable, but sounds slightly less smooth/neutral.

If you want a very natural alternative, you can also say:

Moje dcera je dnes také unavená a chce spát.

Can I use dneska instead of dnes? Is there any difference?

Yes, you can say:

Dnes je moje dcera také unavená…
Dneska je moje dcera také unavená…

Both mean today.

Difference:

dnes – neutral, slightly more formal, common in writing and standard speech
dneska – more colloquial, very common in spoken Czech

So in everyday conversation, dneska is extremely frequent.

Do I have to use je here, or can I drop it like in some languages?

In a normal, full Czech sentence in the present tense, you do use the verb být (je) between the subject and the adjective/noun:

Moje dcera je unavená. – My daughter is tired.

Leaving out je would sound like a headline, fragment, or very telegraphic style:

Moje dcera unavená. – like a note/label, not a normal sentence

So in standard Czech, keep je:

Dnes je moje dcera také unavená a chce spát. ✅
Dnes moje dcera také unavená a chce spát. ❌ (wrong in normal usage)