Uprostřed dvora stoupá z grilu kouř.

Because uprostřed is followed by the genitive case.

• dictionary form: dvůr = courtyard, yard
• genitive singular: dvora

So:

• uprostřed dvora = in the middle of the yard/courtyard

This is a very common pattern in Czech:

• uprostřed města = in the middle of the city
• uprostřed lesa = in the middle of the forest

Uprostřed means in the middle of or amid/in the center of.

It is often used with the genitive:

• uprostřed dvora = in the middle of the yard
• uprostřed místnosti = in the middle of the room

It describes location, not movement.

Because the preposition z means from / out of, and it also requires the genitive case.

• dictionary form: gril
• genitive singular: grilu

So:

• z grilu = from the grill

Compare:

• z domu = from the house
• z kuchyně = from the kitchen

Because the subject is kouř, and kouř is singular.

• kouř = smoke
• stoupá = rises / is rising

So the verb agrees with kouř:

• kouř stoupá = smoke rises

If the subject were plural, the verb would be plural too:

• mraky stoupají = clouds rise

Stoupá is:

• 3rd person singular
• present tense
• from the verb stoupat = to rise, to go up, to ascend

So it literally means:

• it rises
• or, more naturally here, is rising

In Czech, the present tense can often translate either as a general statement or as something happening right now, depending on context.

Czech word order is flexible, and it often puts new or important information later in the sentence.

So:

• Uprostřed dvora stoupá z grilu kouř.

first sets the scene:

• uprostřed dvora = in the middle of the yard
• z grilu = from the grill

and then gives the key noun:

• kouř = smoke

A more neutral English-like order would be:

• Kouř stoupá z grilu uprostřed dvora.

Both are possible in Czech, but they have slightly different emphasis.

Yes.

Czech present tense often covers both:

• a general present: smoke rises
• an ongoing action: smoke is rising

Here, in context, English would usually prefer:

• Smoke is rising from the grill in the middle of the yard.

But the Czech form itself does not separately mark progressive aspect the way English does.

Yes. Kouř is a masculine inanimate noun.

Its basic forms include:

• nominative singular: kouř
• genitive singular: kouře

In this sentence, kouř is in the nominative singular because it is the subject.

Because Czech has no articles.

So kouř can mean:

• smoke
• the smoke
• sometimes even a smoke

The exact meaning depends on context.

Likewise:

• z grilu can mean from the grill
• from a grill

English needs articles; Czech usually does not.

Not with the same meaning.

• uprostřed dvora specifically means in the middle of the yard
• ve dvoře would mean something more like in the courtyard, focusing only on location inside it

So uprostřed dvora is more precise here. It tells you where in the yard the smoke is rising.

It can be either, depending on context.

Dvůr often means:

• yard
• courtyard
• sometimes an enclosed open area near a building

So uprostřed dvora could be:

• in the middle of the yard
• in the middle of the courtyard

Both are possible translations.

A helpful breakdown is:

• Uprostřed dvora = location
• stoupá = verb
• z grilu = source/origin
• kouř = subject

So the sentence is not built in the most English-like order, but it is perfectly natural in Czech.

You can think of it as:

• In the middle of the yard, from the grill, rises smoke.

That sounds poetic in English, but in Czech this kind of ordering is normal.