kape ap annaepane yeongeopsigani jeokhyeo isseo.

카페 앞 literally means “in front of the café.”
In Korean, location nouns like 앞/뒤/위/아래/옆 can appear as:

• N + 앞 (just the noun phrase: “the front of N / in front of N”)
• N + 앞에 (the noun phrase + the location particle 에: “at/in front of N”)

In your sentence, 앞 is immediately followed by 안내판에, so 카페 앞 (에 있는) 안내판에… is understood:
“On the signboard (that is) in front of the café…”
So 카페 앞 안내판에 is a natural “stacking” of nouns: [café-front] [signboard]-on…

에 marks a location where something exists or is written/posted.
So 안내판에 means “on the signboard / on the notice board.”
It’s the place where the information is found.

안내판 is a general word for an informational sign/board that guides or informs people (e.g., directions, rules, hours). Depending on context, it can be translated as sign, information board, or notice board.

이/가 is often used to introduce new information or to simply state a fact:

• 영업시간이 적혀 있어. = “The business hours are written (there).”

If you used 은/는, it would sound more like a contrast or emphasis on that topic:

• 영업시간은 적혀 있어. = “As for the business hours, they’re written (but maybe other info isn’t).”

Both can be possible, but 이/가 is the neutral, straightforward choice here.

적혀 있어 describes a state: something is written and remains written.

• Base verb: 적다 = “to write down”
• Passive form: 적히다 = “to be written”
• Resulting state: 적혀 있다/적혀 있어 = “is written (and is currently in that written state)”

So it’s not simply past tense. It’s more like: “It’s written up / It’s written there.”

They’re very similar, but nuance and formality differ:

• 적혀 있어: “(It’s) written (down)” — common, natural, slightly “noted/recorded” 느낌.
• 써 있어 (from 쓰다): “(It’s) written” — also very common; can feel more general about visible writing.
• 적혀 있다: same meaning as 적혀 있어, but dictionary/plain style; sounds a bit more “complete”/neutral in writing.

In casual speech, 있다 → 있어 is very normal:

• 적혀 있다 (plain)
• 적혀 있어 (casual spoken)

있어 is casual/informal speech (used with friends, people younger than you, close relationships).
The polite version would be:

• 카페 앞 안내판에 영업시간이 적혀 있어요.

Even more formal:

• …적혀 있습니다.

Yes. Korean word order is flexible because particles show roles.
Both are natural:

• 카페 앞 안내판에 영업시간이 적혀 있어.
• 영업시간이 카페 앞 안내판에 적혀 있어.

The first one sets the scene first (on the signboard…), then states what’s written. The second highlights 영업시간 earlier.

Yes—Korean often omits words that are understood from context.
This sentence implicitly means something like:

• (카페 앞에 있는) 안내판에 영업시간이 적혀 있어.
  = “On the signboard (that is) in front of the café, the business hours are written.”

Also, the speaker might be implying 봐/보면 (“if you look”):

• “If you look at the sign in front of the café, the hours are written there.”

In natural speech, it’s often pronounced smoothly as:

• 적혀 있어 → [저켜 이써] (approx.)

Also note:

• 영업시간 is pronounced close to [영업씨간] because ㅂ + 시 often sounds like ㅄ/ㅆ-like tensification in fast speech. (You’ll commonly hear 영업씨간.)