Valaki a téren áll és vár.

-en is the superessive suffix variant used here: tér → téren (“on/at the square”). Very roughly:

• Back-vowel words often take -on (e.g., hajó → hajón, “on the boat”).
• Front rounded-vowel words often take -ön (e.g., tükör → tükrön, “on the mirror”).
• Many front unrounded-vowel words take -en (e.g., szék → széken, “on the chair”; tér → téren).

There are exceptions (e.g., híd → hídon), and the choice also aims for easy pronunciation. It’s best to learn common place nouns with their typical superessive form.

You normally use an article with a specific place:

• Valaki a téren áll és vár. = “Someone is standing and waiting in the square.” (a specific, known square) If you don’t care which square, you can say:
• Valaki egy téren áll és vár. = “Someone is standing and waiting in a square.” Dropping the article entirely (Valaki téren...) is usually not idiomatic; use a (the) or egy (a).

-ban/-ben (inessive) is “in, inside” something enclosed. A tér is an open area, so Hungarian uses the superessive: téren (“on/at the square”). Compare:

• a parkban = “in the park” (enclosed area)
• a hídon = “on the bridge”
• a téren = “in/on the square”

Hungarian word order highlights information. The item immediately before the verb is in focus. In Valaki a téren áll és vár, the location a téren is in the focus slot, subtly emphasizing “at the square (as opposed to elsewhere).” More neutral options include:

• Valaki áll és vár a téren. (location after the predicate)
• A téren valaki áll és vár. (sets the scene: “At the square, someone is standing and waiting.”) All are grammatical; the difference is nuance and emphasis.

It can mean either. Hungarian simple present covers both habitual and ongoing actions. Context usually makes it clear. If you want to emphasize the ongoing nature, add words like éppen or most:

• Valaki éppen a téren áll és vár. = “Someone is standing and waiting in the square right now.”

The subject valaki (“someone”) is third person singular, and there’s no direct object, so you use the indefinite (subject) conjugation:

• ő/valaki áll (“he/she/someone stands”)
• ő/valaki vár (“he/she/someone waits”) This is the regular 3rd person singular indefinite present.

Use the plural subject valakik with plural verb forms:

• Valakik a téren állnak és várnak. = “Some people are standing and waiting in the square.”

Vár can stand alone (“wait”) or take a complement:

• With the sublative: vár valamire/valakire (e.g., Buszra várok. = “I’m waiting for the bus.”)
• With a direct object (more formal/literary or with pronouns): Várom a buszt.; Várlak. = “I’m waiting for you.” In your sentence, vár is fine without specifying what for.

Not with valaki. Valaki itself is the subject (“someone”). Ő (“he/she”) refers to a specific known person. If you mean a specific person, you could say:

• Ő a téren áll és vár. = “He/She is standing and waiting in the square.”

Yes. Áll és vár literally describes the posture plus the act of waiting. Várakozik is an intransitive verb meaning “to wait, to be in a state of waiting,” often a bit more formal or procedural:

• Valaki a téren várakozik. = “Someone is waiting in the square.”
• Valaki a téren áll és vár. paints a more physical picture (standing, waiting).

Place nem before each verb, or focus the negation:

• General negation: Valaki a téren nem áll és nem vár. = “Someone is not standing and not waiting in the square.”
• Negating the location (focus): Valaki nem a téren áll és vár. = “Someone is standing and waiting, but not in the square.”