Můj telefon teď nejde, proto ti píšu e-mail.

In Czech, jít normally means to go, but it is also commonly used for machines, devices, programs, or systems in the sense of working / functioning / running.

So:

• Telefon nejde. = The phone isn’t working.
• Televize nejde. = The TV doesn’t work / isn’t on.
• Internet nejde. = The internet isn’t working.

This is very natural Czech. English uses work, while Czech often uses jít in these contexts.

Můj means my, and it agrees with telefon in gender, number, and case.

• telefon is masculine inanimate
• nominative singular form of my = můj

So:

• můj telefon = my phone

Czech often leaves out possessives when the meaning is obvious, but including můj is perfectly normal here, especially if you want to emphasize that it is your phone that is not working.

Czech often does not use a present-tense form of to be where English would.

In English:

• My phone is not working.

In Czech:

• Můj telefon teď nejde.

There is no separate word for is because the verb nejde already carries the present-tense meaning.

This is normal in Czech: present-tense verbs usually stand on their own without an extra auxiliary like English is.

Teď means now / at the moment / right now.

In this sentence:

• Můj telefon teď nejde = My phone isn’t working right now

Its position is fairly flexible, because Czech word order is more flexible than English word order. For example, these are all possible:

• Můj telefon teď nejde.
• Teď můj telefon nejde.
• Můj telefon nejde teď.
  (possible, but usually sounds marked or contrastive)

The version in your sentence sounds natural and neutral.

Proto means something like therefore, so, because of that, or that’s why, depending on context.

In this sentence:

• Můj telefon teď nejde, proto ti píšu e-mail.
• My phone isn’t working right now, so / therefore / that’s why I’m writing you an email.

It links the first clause to the consequence in the second clause.

A very common conversational alternative is:

• ..., tak ti píšu e-mail.

But proto is slightly more explicit and a bit more formal or careful in tone.

Because ti is the dative form of ty (you, singular informal), and here it means to you.

The verb psát often works like this:

• psát komu? co? = to write to someone something

So in the sentence:

• ti = to you
• e-mail = an email

That gives:

• píšu ti e-mail = I’m writing you an email / I’m writing an email to you

Compare:

• tě = accusative form, used for direct objects
• tebe = a stressed form, often used after prepositions or for emphasis
• ti = dative, used here because you is the indirect object

Yes, but ti is a short unstressed form called a clitic, and clitics in Czech usually go in the second position of the clause.

So in:

• proto ti píšu e-mail

the first element is proto, and ti comes right after it.

This is very typical Czech word order.

You may also hear:

• Píšu ti e-mail.

Here the first element is píšu, so ti comes second.

You generally would not put ti in a strongly stressed position unless you had a special reason.

The infinitive is psát = to write. Its present tense is irregular in form:

• já píšu = I write / I am writing
• ty píšeš
• on/ona píše
• my píšeme
• vy píšete
• oni píšou / píší

So píšu is simply the correct 1st person singular present form.

Two things are worth noticing:

1. The vowel changes: psát → píšu
2. Czech spelling uses š here, not plain s

This is a verb you just need to learn as part of its conjugation pattern.

Because Czech usually drops subject pronouns when the verb ending already makes the subject clear.

• píšu already means I write / I am writing

So:

• píšu e-mail = I’m writing an email

You can add já for emphasis, contrast, or clarity:

• ...proto já ti píšu e-mail.

But in neutral speech, leaving it out is more natural.

It is the direct object, so it is in the accusative case.

However, e-mail is masculine inanimate, and in the singular the accusative form is the same as the nominative form.

So:

• nominative: e-mail
• accusative: e-mail

That is why the word does not change its ending here.

Yes. In everyday modern Czech, telefon very often means a mobile phone / cell phone, unless the context suggests otherwise.

If someone wants to be more specific, they might say:

• mobil = mobile phone
• mobilní telefon = mobile phone

But můj telefon teď nejde naturally sounds like my phone isn’t working right now, and most people would understand that as a mobile phone unless the situation suggests another kind of phone.

Yes, both spellings are used.

• e-mail is very common
• email is also widely seen and accepted in many contexts

In actual use, Czech speakers also often just say:

• mail

But in learner materials and careful writing, e-mail is very normal.

Yes, absolutely.

• Můj telefon teď nejde.
• Můj telefon teď nefunguje.

Both can mean My phone isn’t working right now.

The difference is mostly nuance:

• nejde is very common and idiomatic in everyday speech
• nefunguje is a bit more explicit, since it literally means doesn’t function

Both are correct and natural.