Kašel je v noci horší, proto moje maminka často nemůže spát.

Yes. In this sentence, je means is, and Czech normally uses the verb být (to be) in the present tense when describing something with an adjective.

So:

• Kašel je horší = The cough is worse

Unlike in some languages, you cannot usually leave out je here in standard Czech.

Kašel (cough) is a masculine inanimate noun.

That matters because adjectives and some other words agree with the noun. Here, however, the adjective is in the predicate after je, so you mainly just need to know that kašel is the subject:

• Kašel je horší = The cough is worse

A learner may also notice that kašel ends in a consonant, which is common for masculine nouns.

Because the preposition v (in) often requires the locative case when it means location.

The noun is:

• noc = night

In the locative singular, it becomes:

• v noci = at night / during the night / in the night

So:

• v noci literally means in the night, but in natural English here it is usually translated as at night.

Horší means worse. It is the comparative form of špatný (bad).

So:

• špatný = bad
• horší = worse

In this sentence:

• Kašel je v noci horší = The cough is worse at night

Czech comparatives do not always look predictable, and horší is one of those forms you should just memorize.

Because the sentence does not explicitly say worse than something. It just says the cough is worse at night.

Compare:

• Kašel je v noci horší. = The cough is worse at night.
• Kašel je v noci horší než přes den. = The cough is worse at night than during the day.

So horší does not have to be followed by než (than).

Proto here means therefore / so / that is why.

It is not the same as protože, which means because.

Compare:

• Kašel je v noci horší, proto moje maminka často nemůže spát.
  = The cough is worse at night, therefore my mother often cannot sleep.

• Moje maminka často nemůže spát, protože kašel je v noci horší.
  = My mother often cannot sleep because the cough is worse at night.

So:

• proto = therefore / so / that is why
• protože = because

This is a very common thing for learners to confuse.

Yes, both are possible.

• moje maminka = my mommy / my mum / my mother
• má maminka = my mommy / my mum / my mother

In many contexts, moje and má are both acceptable as forms of my.

A small style note:

• maminka sounds warm, affectionate, and personal, like mum or mommy
• matka is more neutral or formal: mother
• máma/mama is very common and informal: mum/mom

So moje maminka sounds natural and caring.

Často means often, and its position is very natural here.

• moje maminka často nemůže spát = my mother often cannot sleep

Czech word order is more flexible than English word order, but adverbs like často are commonly placed before the main verb phrase.

Other word orders can be possible, but they may sound different in emphasis:

• Moje maminka často nemůže spát. = neutral
• Moje maminka nemůže často spát. = may sound more like she cannot sleep often / she does not get to sleep often, which is a bit different

So the given order is the most straightforward one for the intended meaning.

This is a very common Czech pattern:

• nemůže = cannot / is not able to
• spát = to sleep

Together:

• nemůže spát = cannot sleep

The verb moci means can / to be able to, and after it Czech uses an infinitive:

• může spát = can sleep
• nemůže spát = cannot sleep

So it works very much like English can + verb.

In Czech, negation with verbs is usually formed by adding ne- directly to the verb.

So:

• může = can
• nemůže = cannot

This is standard Czech spelling. Unlike English, which often writes cannot or can not depending on the structure, Czech normally attaches the negative particle to the verb.

More examples:

• má = has

• nemá = does not have

• je = is
• není = is not

Spát is imperfective.

That fits perfectly here, because the sentence is about an ongoing activity or state:

• nemůže spát = cannot sleep

In Czech, imperfective verbs are typically used for general, repeated, or ongoing actions. Since this sentence describes a recurring problem at night, spát is exactly what you would expect.

Yes. Czech word order is flexible, and you can rearrange the sentence depending on emphasis.

For example:

• Kašel je v noci horší, proto moje maminka často nemůže spát.
  Focus starts with the cough.

• Moje maminka často nemůže spát, protože kašel je v noci horší.
  Focus starts with the mother not being able to sleep.

Both are correct, but they organize the information differently. The original sentence first presents the cause and then the result.

A rough pronunciation guide is:

• Kašel je v noci horší, proto moje maminka často nemůže spát.

Approximate English-style pronunciation:

• KAH-shell yeh v NOT-see HOR-shee, PROH-toh MOH-yeh MAH-min-kah CHAS-toh NEM-oo-zheh spaht

A few useful notes:

• š sounds like sh
• č sounds like ch in chair
• ž sounds like the s in measure
• c sounds like ts
• á, í, ů are long vowels

You do not need to pronounce it exactly like the English guide above, but it can help you get started.