Grădina vecinului este plină de flori colorate.

Romanian marks possession with case endings, not an apostrophe. Here:

• vecinului is the genitive form of vecinul (the neighbor).
• grădina vecinului literally means “the garden of the neighbor.”
  There’s no apostrophe—possession is clear from the ending -ului on vecin.

Romanian uses enclitic articles attached to the end of nouns:

• Feminine nouns add -a (e.g. grădină → grădina).
• Masculine nouns add -ul (e.g. vecin → vecinul).
  So grădină (garden) + -a = grădina (the garden).

vecinului is in the genitive (also identical to the dative) singular masculine:

• Genitive expresses “of the neighbor.”
• The ending -ului shows both definiteness and the possessive relation.
  Thus grădina vecinului = “the garden of the neighbor.”

Adjectives in Romanian agree in gender and number with the noun they describe:

• grădina is feminine singular.
• The masculine form plin becomes plină to match.
  Hence grădina este plină = “the garden is full.”

When saying “full of” something, Romanian typically uses plin/plină + de + [noun]:

• plină de flori = “full of flowers.”
  Using cu (with) is less common in this idiom and can change nuance.

Adjectives must agree with the noun in both gender and number:

• flori is feminine plural (indefinite).
• The adjective colorat (colored) takes the feminine plural ending -e → colorate.
  So flori colorate = “colored flowers.”

In Romanian, descriptive adjectives usually follow the noun:

• flori colorate (flowers colored)
  You can move some adjectives before the noun for emphasis or poetic effect, but the neutral order is noun → adjective.

Yes. este is the full third-person singular of a fi (to be). e is its common contracted form:

• Grădina vecinului este plină… (more formal/written)
• Grădina vecinului e plină… (colloquial/spoken)
  Both mean the same; choose este for formality and e for casual speech.