A próbanap holnap lesz.

• a = the
• próbanap = trial day, test day, or sometimes probation day, depending on context
• holnap = tomorrow
• lesz = will be

So the sentence literally comes out as The trial day tomorrow will be, but natural English is The trial day will be tomorrow or simply The trial day is tomorrow.

Because Hungarian very often forms compounds by joining words together.

Here:

• próba = trial, test, rehearsal
• nap = day

So próbanap is a compound noun. This is very normal in Hungarian.

A is the definite article, meaning the.

It is used here because the speaker has a specific trial day in mind, not just any trial day. In that sense, it works much like English the.

So:

• A próbanap = the trial day
• Egy próbanap = a trial day

Lesz is the 3rd person singular future form of lenni, which means to be.

A very useful mini-paradigm is:

• van = is
• volt = was
• lesz = will be

So in this sentence:

• A próbanap holnap lesz. = The trial day will be tomorrow.

Because with to be, Hungarian normally just uses lesz.

Hungarian can form the future with fog + infinitive, but with lenni, the form lesz is the usual and natural choice.

So:

• natural: holnap lesz
• much less natural here: holnap fog lenni

In this sentence, lesz is exactly what you would expect.

Yes.

Even though lesz is formally future, English often prefers is tomorrow for scheduled events. So both of these are good translations, depending on style:

• The trial day will be tomorrow.
• The trial day is tomorrow.

Yes, that is also possible.

Hungarian often uses the present tense for planned or scheduled future events, just like English does in sentences such as The meeting is tomorrow.

So both can work:

• A próbanap holnap van.
• A próbanap holnap lesz.

Very roughly:

• van can sound a bit more like a scheduled fact
• lesz makes the future sense more explicit

But in many contexts, both are natural.

Hungarian does often omit the verb van in the 3rd person singular present, but only in certain sentence types.

For example:

• A próbanap fontos. = The trial day is important.
  • no van

But in your sentence:

• lesz is future, so it cannot be omitted

Also, if you use the present version A próbanap holnap van, the van stays. With time/location-type predicates, Hungarian normally keeps van.

That is a normal Hungarian word order.

Hungarian word order is flexible, but it is not random. In a neutral sentence, time expressions often come before the verb, so holnap lesz sounds very natural.

Your sentence:

• A próbanap holnap lesz.

Other word orders are possible, but they change the emphasis:

• Holnap lesz a próbanap. = stronger focus on tomorrow
• A próbanap lesz holnap. = more marked, less neutral in most contexts

So the given order is a very standard one.

Holnap is a time adverb meaning tomorrow.

In this sentence, it does not need any case ending. It already means tomorrow by itself.

Related form:

• holnapi = tomorrow's

Example:

• a holnapi próbanap = tomorrow's trial day

A rough pronunciation guide is:

• a = short aw
• próbanap = PROH-baw-nop
• holnap = HOL-nop
• lesz = less

A few useful notes:

• Stress is on the first syllable of each word in Hungarian.
• ó is a long vowel.
• Hungarian spelling is very regular, so once you learn the sounds, pronunciation becomes predictable.