A műhely ma reggel nyitva van.

A is the Hungarian definite article, so it means the.

A useful extra point:

• Hungarian uses a before consonant sounds
• Hungarian uses az before vowel sounds

So:

• a műhely = the workshop
• az iskola = the school

Because műhely is the subject of the sentence, and Hungarian subjects are normally in the basic dictionary form, with no special ending.

So here:

• a műhely = the workshop
• it is the thing that is open

Hungarian does not add a nominative ending for the subject.

Ma reggel means this morning.

Literally, it is:

• ma = today
• reggel = in the morning / morning

So word-for-word it is something like today morning, but the natural English translation is this morning.

Because some time words in Hungarian often work adverbially in a simple fixed form, without an extra case ending.

For example:

• reggel = in the morning
• este = in the evening
• délelőtt = in the late morning / before noon

So ma reggel is a normal, idiomatic time expression.

Literally, nyitva van is something like is in an open state.

It has two parts:

• nyitva = open in the sense of opened / left open
• van = is

Together, nyitva van is the standard Hungarian way to say that a place, shop, door, etc. is open.

A very common pair is:

• nyitva van = is open
• zárva van = is closed

That is a very good question.

In Hungarian, the verb to be is often omitted in the present tense, third person singular, especially with simple noun or adjective predicates:

• A műhely nagy. = The workshop is big.

But in expressions like nyitva van, the van is normally kept.
That is because nyitva is part of a set expression describing a state, not just a simple ordinary adjective in the same way as nagy.

So:

• A műhely nagy. = no van
• A műhely nyitva van. = van stays

Sometimes nyitott can also mean open, but nyitva van is the most natural everyday way to say that a place is open at a certain time.

So for opening status, Hungarian usually prefers:

• A műhely nyitva van.

By contrast, nyitott can sound more like an adjective meaning:

• opened
• open
• open-minded
• not closed off

So for a business or workshop being open right now, nyitva van is the safer and more idiomatic choice.

No. Hungarian word order is fairly flexible, and changing the order often changes the emphasis rather than the basic meaning.

The sentence:

• A műhely ma reggel nyitva van.

is a neutral, natural order.

Other orders are possible, for example:

• Ma reggel a műhely nyitva van.
  This puts more focus on this morning.

• Nyitva van a műhely ma reggel.
  This gives more prominence to the fact that it is open.

So the original version is a good neutral model, but it is not the only possible order.

Műhely is pronounced approximately myoo-hey, but that English approximation is not perfect.

More accurately:

• mű has a long front rounded vowel, like German ü if you know it
• h is pronounced normally
• ely sounds roughly like ej

A rough pronunciation guide is:

• műhely ≈ MYUU-hey

Also, the Hungarian ly is pronounced like j in modern standard Hungarian.

Usually it means open for business / operating, especially because it refers to a time expression: this morning.

With places such as shops, offices, or workshops, nyitva van very often means that the place is open and functioning at that time.

Depending on context, it could also mean literally open, but the most likely meaning here is:

• the workshop is open this morning
• it is not closed this morning