Hay paz en el bosque.

• Está (from estar) describes location or temporary states: e.g. El árbol está en el bosque (“The tree is in the forest”).
• Es (from ser) describes identity or permanent qualities: e.g. La paz es importante (“Peace is important”).
  To say “there is/are” in Spanish you almost always use hay.

• Bosque is a countable, singular noun, so Spanish normally requires an article: el bosque = “the forest.”
• You can’t say en bosque without an article.
• If you meant “in a forest” (any forest) you’d say en un bosque; but to speak of “the forest” or forests in general, el bosque is standard.

Bosque is masculine: it takes el. Unfortunately, many Spanish noun genders must be memorized. A few guidelines:
• Nouns ending in ​-o are often masculine.
• Abstract nouns ending in ​-e can be either gender.
In this case you simply learn el bosque.

A rough phonetic guide:
• Hay = [ai] (like “eye” but with an h sound in the back)
• paz = [pas] (short “a,” z sounds like [s])
• en = [en]
• el = [el]
• bosque = [ˈbos.ke] (stress on the first syllable)
Put it all together: [ai pas en el ˈbos.ke].

Yes, that’s perfectly correct. Spanish word order is flexible.
• Hay paz en el bosque. (neutral)
• En el bosque hay paz.
By fronting en el bosque you emphasize where the peace is.

You’d use the imperfect of haber:
• Había paz en el bosque. (ongoing or background state)
If you mean a one-time, completed event you could also say
• Hubo paz en el bosque.

In Spanish you wrap the sentence with question marks and invert the intonation:
¿Hay paz en el bosque?