A közösségi program jól sikerül.

Közösségi program is a noun phrase meaning something like community event, community activity, or community program, depending on context.

• közösség = community
• közösségi = community-related, communal
• program = program, event, activity, schedule item

So közösségi program is literally community-related program/event.

Hungarian has two forms of the definite article:

• a
• az

Which one you use depends on the sound at the beginning of the next word:

• a before a consonant sound
• az before a vowel sound

Since közösségi starts with k, a consonant, you say a közösségi program.

Because jól is the adverb form, and here it modifies the verb sikerül.

• jó = good
• jól = well

In English, compare:

• a good event → adjective
• the event goes well → adverb

In this sentence, the idea is the community event turns out well / succeeds well, so Hungarian uses jól.

Sikerül comes from the verb sikerülni, which often means:

• to succeed
• to turn out well
• to go well
• sometimes to manage to in other sentence patterns

In this sentence, it means something like:

• The community event goes well
• The community event turns out well
• The community event is successful

A very important point: sikerülni does not work exactly like English to succeed in every situation, so it is best learned as its own Hungarian pattern.

Yes. A közösségi program is the subject.

So the structure is:

• A közösségi program = the community event/program
• jól sikerül = goes well / turns out well

There is no direct object here. The sentence is about what happens to the event.

Sikerül is:

• present tense
• third person singular
• from the dictionary form sikerülni

So it literally corresponds to it succeeds / it turns out well.

Because program is singular, the verb is singular too.

It actually does show the subject. In Hungarian, verb endings often indicate the person and number.

Here:

• sikerülök = I succeed / turn out well
• sikerülsz = you succeed
• sikerül = he/she/it succeeds

Since a közösségi program is a singular third-person subject (it), sikerül is the correct form.

The given order is neutral and natural:

• A közösségi program jól sikerül.

But Hungarian word order is flexible and often used for focus or emphasis.

For example:

• Jól sikerül a közösségi program.
  This puts more attention on jól (it goes well).

The original sentence is a straightforward neutral statement.

Grammatically, it is present tense.

However, in Hungarian, present tense can sometimes be used in a broader way depending on context. Still, in many real-life situations, if you mean a future event, speakers often prefer something like:

• A közösségi program jól fog sikerülni. = The community event will go well.

And if the event already happened:

• A közösségi program jól sikerült. = The community event went well.

So the sentence as written is present tense, but the exact time reference depends on context.

They are related, but not the same structure.

• A program sikeres. = The event is successful.
  This uses sikeres, an adjective meaning successful.

• A program jól sikerül. = The event turns out well / goes well.
  This uses the verb sikerülni.

So:

• sikeres describes the result as a quality
• jól sikerül describes how the event turns out

Both can be natural, but they are built differently.

Közösségi is an adjective formed from the noun közösség (community) with the suffix -i, which often means related to or belonging to.

So:

• közösség = community
• közösségi = community-related

In this sentence, it modifies program.

Hungarian adjectives do not agree with nouns in gender, and there is no grammatical gender in Hungarian. So közösségi stays the same here.

Because the main verb is sikerül. This is not an X is Y sentence. It is a full verb meaning succeeds / goes well / turns out well.

So the sentence is not:

• The community event is good

It is more like:

• The community event goes well

That is why no separate verb like is appears.