Läraren skriver en bokstav med krita på tavlan.

Because läraren is the definite singular form of lärare (teacher).

• en lärare = a teacher
• läraren = the teacher

In Swedish, the definite article is usually added as an ending, not written as a separate word like English the.

So:

• lärare = teacher
• läraren = the teacher

Because en bokstav means a letter.

Swedish usually uses an article in the singular when English would use a/an:

• en bokstav = a letter

Here, bokstav is a common-gender noun, so it takes en in the indefinite singular.

Compare:

• en bokstav = a letter
• bokstaven = the letter

In this sentence, bokstav means a letter of the alphabet.

That makes sense with the context:

• skriver en bokstav = writes a letter/character
• på tavlan = on the board

If you mean a letter sent by post, Swedish usually uses brev:

• ett brev = a letter (mail)

So:

• bokstav = letter of the alphabet
• brev = letter in the mail

Med krita means with chalk, and here krita is being used more like a material or writing medium than as one specific countable object.

So the sentence focuses on how the teacher writes:

• med krita = with chalk

If you said med en krita, that would sound more like with a piece of chalk / with one chalk stick, emphasizing a single object.

Both can be possible in the right context, but med krita is very natural when talking about writing on a board.

Because på means on, and tavlan means the board.

So:

• på tavlan = on the board

Again, Swedish shows definiteness with an ending:

• en tavla = a board / picture / panel
• tavlan = the board

In a classroom context, tavlan usually means the board, such as a blackboard or whiteboard.

This is the normal Swedish word order for a simple statement:

subject + verb + object + other information

So here:

• Läraren = subject
• skriver = verb
• en bokstav = object
• med krita = means/instrument
• på tavlan = place

A very natural English-like breakdown is:

• The teacher / writes / a letter / with chalk / on the board

Swedish word order is often quite similar to English in basic main clauses.

It can mean both, depending on context.

Swedish present tense often covers both:

• writes
• is writing

So Läraren skriver en bokstav can mean:

• The teacher writes a letter
• The teacher is writing a letter

Swedish does not usually need a separate progressive form like English is writing.

The infinitive is skriva, which means to write.

Common forms are:

• skriva = to write
• skriver = writes / is writing
• skrev = wrote
• skrivit = written

So in the sentence, skriver is the present tense form.

A rough English-friendly guide is:

• lärare ≈ LEH-ra-reh
• bokstav ≈ BOOK-stahv
• tavlan ≈ TAHV-lan

A few helpful notes:

• ä sounds somewhat like the vowel in bed, but not exactly the same.
• The r in Swedish is not usually the same as a strong American English r.
• a in tavlan is longer and more open than English a in cat.

Also, lärare has two r sounds, and the final -e is pronounced, unlike in English.

No. Tavla can have several related meanings, depending on context.

It can mean:

• a board
• a sign
• a painting
• a picture
• a classroom board

In this sentence, because of skriver and med krita, tavlan clearly means the board in a classroom.

So context tells you which meaning is intended.

Yes, but it would mean something different.

• en bokstav = a letter
• bokstaven = the letter

So:

• Läraren skriver en bokstav med krita på tavlan = The teacher writes a letter with chalk on the board.
• Läraren skriver bokstaven med krita på tavlan = The teacher writes the letter with chalk on the board.

The first introduces an unspecified letter; the second refers to a specific letter already known from context.