Nisipul de pe plajă este cald.

In Romanian, the definite article (“the”) is not a separate word but is enclitic—attached at the end of the noun. For masculine singular nouns ending in a consonant, you add -ul:

• nisip (sand) + -ul → nisipul (the sand)

de pe is a compound preposition meaning “from off” or “off the surface of.”

• de alone means “from” (a general origin).
• pe alone means “on” (a location on a surface).
  Together, de pe conveys “originating from the top of,” so de pe plajă = “off the beach.”

In Romanian:

• pe
  • location indicates being on a surface (e.g. pe masă = “on the table”).
• în
  • location indicates being inside something (e.g. în cameră = “in the room”).
    A beach is treated as a surface, so you say pe plajă = “on the beach.”

When expressing location with pe in an indefinite or general sense, Romanian usually omits the article.

• pe plajă = “on (a/the) beach” in general.
  If you want to specify a particular beach, you could say pe plaja aia = “on that beach.”

Not exactly.

• nisip de plajă can mean “beach sand” as a type or category.
• In Romanian, generic statements (like “Beach sand is warm”) normally use the definite article on the subject: Nisipul de plajă este cald.
• Omitting de pe removes the nuance of “coming off the surface” and just labels the sand type.

e is a colloquial contraction of este (the verb “to be”).

• In informal speech you often hear e cald.
• In writing and in more formal contexts, you use the full form este.

Romanian adjectives agree in gender and number with the noun they modify.

• nisip is a masculine singular noun.
• The matching masculine singular adjective is cald.
  (If the noun were feminine singular, it would be caldă; masculine plural calzi, feminine plural calde.)

The letter ă is a schwa (an “uh” sound), similar to the ‘a’ in English sofa.

• plajă sounds like [ˈplaʒə], where the final ă is the unstressed schwa.

Yes.

• nisipul plajei literally means “the sand of the beach,” using the genitive (plajei = “of the beach”).
• nisipul de pe plajă emphasizes location: “the sand that is on the beach.”
  The first frames possession/association, the second highlights origin from a surface.

Whenever you want to express movement or removal “off the surface of” something, you use de pe.
Examples:

• de pe masă = “off the table”
• de pe raft = “off the shelf”
  If you use din, it means “from inside/of” (din casă = “from inside the house”).