Dnes mám hotovost, proto nemusím platit kartou.

Yes. Dnes means today.

Czech often places a time expression near the beginning of the sentence if it sets the scene for everything that follows. So:

• Dnes mám hotovost... = Today I have cash...

There is no preposition here. English says today on its own too, and Czech works the same way.

You could move dnes elsewhere, but the beginning is very natural:

• Dnes mám hotovost.
• Mám dnes hotovost.

Both are possible, but the first one sounds more like As for today...

Mám hotovost means I have cash or I have cash on me / available in cash.

The noun hotovost specifically refers to cash.
By contrast, peníze means money in general.

So:

• mám peníze = I have money
• mám hotovost = I have cash

That difference matters here, because the second clause talks about not needing to pay by card. So hotovost is the more precise word.

It is in the accusative, because it is the direct object of mám (I have).

The verb mít usually takes an accusative object:

• mám knihu = I have a book
• mám čas = I have time
• mám hotovost = I have cash

A useful detail: for this noun, nominative singular and accusative singular look the same:

• nominative: hotovost
• accusative: hotovost

So even though the form does not change, the function is still accusative.

Proto means therefore, that’s why, or for that reason.

It introduces the result of the first clause:

• Dnes mám hotovost, proto nemusím platit kartou.
• Today I have cash, therefore I don’t have to pay by card.

So the logic is:

1. I have cash today.
2. Therefore I do not need to pay by card.

This is a very common question.

• proto = therefore / that’s why → gives the result
• protože = because → gives the reason

Compare:

• Dnes mám hotovost, proto nemusím platit kartou.
  = Today I have cash, therefore I don’t have to pay by card.

• Nemusím platit kartou, protože dnes mám hotovost.
  = I don’t have to pay by card because I have cash today.

Same basic idea, but the structure is different:

• proto points forward to a consequence
• protože introduces the cause

Because the sentence contains two clauses:

1. Dnes mám hotovost
2. proto nemusím platit kartou

In Czech, when two clauses are linked like this, a comma is normally used. So the comma helps show the pause and the logical connection.

It is very natural to write:

• Dnes mám hotovost, proto nemusím platit kartou.

In Czech, negation is usually attached directly to the verb as a prefix:

• musím = I must / I have to
• nemusím = I do not have to / I don’t need to

So Czech does not normally separate the negative particle from the verb the way English does with do not.

This is one of the most important verb patterns in Czech:

• mám → nemám
• jsem → nejsem
• musím → nemusím

No — and this is a very important distinction.

• nemusím = I don’t have to
• nesmím = I must not / I am not allowed to

So in this sentence:

• nemusím platit kartou = I don’t have to pay by card

It does not mean paying by card is forbidden. It only means it is unnecessary, because cash is available.

Compare:

• Nemusím tam jít. = I don’t have to go there.
• Nesmím tam jít. = I must not go there.

Because musím / nemusím is a modal verb, and modal verbs are followed by an infinitive.

So the pattern is:

• musím + infinitive
• nemusím + infinitive

Examples:

• Musím pracovat. = I have to work.
• Nemusím vařit. = I don’t have to cook.
• Nemusím platit kartou. = I don’t have to pay by card.

So platit stays in the infinitive because nemusím is the conjugated verb.

Kartou is the instrumental singular of karta.

Here Czech uses the instrumental to express the means or instrument by which something is done:

• platit kartou = to pay by card

This is similar to English by card, where the card is the method used.

Forms of karta:

• nominative: karta
• accusative: kartu
• instrumental: kartou

So:

• platit kartou = pay by card

If you used kartu, it would not mean the same thing here.

Yes, it is a very common and natural expression.

Some similar expressions are:

• platit kartou = pay by card
• platit hotově = pay in cash
• platit v hotovosti = pay in cash

So in everyday Czech, if someone asks how you want to pay, you might hear or say:

• Můžu platit kartou? = Can I pay by card?
• Budu platit kartou. = I’ll pay by card.
• Zaplatím v hotovosti. = I’ll pay in cash.

They are related, but they are used differently.

• hotovost = cash as a noun
• v hotovosti = in cash as an adverbial phrase

So:

• Mám hotovost. = I have cash.
• Zaplatím v hotovosti. = I will pay in cash.

In your sentence, hotovost is the thing the speaker has.
If the sentence were about the method of payment, Czech would more naturally use v hotovosti or hotově.

Yes. Czech word order is fairly flexible, although some versions are more natural in a neutral context than others.

The original sentence:

• Dnes mám hotovost, proto nemusím platit kartou.

This is very natural and clear.

Other possible versions include:

• Proto dnes nemusím platit kartou, protože mám hotovost.
• Nemusím dnes platit kartou, protože mám hotovost.

But these are not exactly the same in emphasis.

The original version emphasizes:

1. today
2. I have cash
3. therefore no need to pay by card

So the word order helps shape what feels most important.

In informal speech, some speakers do use cash, especially in casual or mixed modern language. But hotovost is the standard Czech word.

So for learners, hotovost is the safer and better choice.

• mám hotovost = standard, correct, neutral
• mám cash = informal, colloquial, more slang-like

If you are learning standard Czech, stick with hotovost.

Yes, it is natural and understandable.

A native speaker might also say things like:

• Dnes mám hotovost, takže nemusím platit kartou.
• Mám dnes hotovost, takže zaplatím hotově.
• Dneska mám hotovost, nemusím platit kartou.

But your original sentence is perfectly normal. It sounds slightly careful or explicit, which is often useful for learners.