Minä tilaan taksin hänelle nyt.

Taksin is the singular total object (often called “genitive/accusative -n”). In an affirmative sentence where you’re ordering one whole, specific taxi, the object gets -n.

• Affirmative, total: Tilaan taksin.
• Negative or incomplete/ongoing: En tilaa taksia. (negative forces partitive)
  Using taksia here in an affirmative statement would sound wrong or at least unusual.

Hänelle is in the allative case (-lle), which often means “to” or “for.” Here it marks a beneficiary: “for him/her.”

• Base pronoun: hän
• Allative: hänelle = “to/for him/her”

Yes; Finnish word order is flexible and used for emphasis/information structure. All of these are natural, with slight differences in focus:

• Tilaan hänelle nyt taksin. (beneficiary early; neutral)
• Tilaan nyt hänelle taksin. (time early)
• Nyt tilaan hänelle taksin. (strong “now” focus)
• Minä tilaan taksin hänelle nyt. (explicit “I,” often contrastive)
  New or emphasized info tends to come later in the sentence.

Both are possible. Finnish present covers English present progressive and near future:

• “I’m ordering now” or “I’ll order now.”
  To emphasize an ongoing action, you can use the -massa form: Olen tilaamassa taksia. To stress near future, add an adverb: Tilaan taksin pian/kohta.

Yes. Nyt can go at the end, the beginning, or earlier in the clause:

• Tilaan hänelle nyt taksin.
• Tilaan nyt hänelle taksin.
• Nyt tilaan hänelle taksin. (strong emphasis on “now”)
  All are fine; placement shifts focus rather than correctness.

Usually no, if you mean “call/order a taxi to come now.”

• Tilata taksi = to order/call a taxi (idiomatic for immediate service).
• Soittaa taksi(n) is also common (“to phone for a taxi”).
• Varata = to reserve/book in advance (hotels, tables, sometimes pre-booked taxis for later): Varaan hänelle taksin huomiseksi.

Replace hänelle with the allative form of the pronoun:

• “for you (sg. informal)”: sinulle → Tilaan sinulle taksin nyt.
• “for you (formal/plural)”: teille → Tilaan teille taksin nyt.
• “for them”: heille → Tilaan heille taksin nyt.

Hän is the standard, gender-neutral “he/she” in formal/written Finnish. In everyday speech, Finns often use se (“it”) for people, with matching case forms:

• Colloquial: Mä tilaan sille nyt taksin.
  Avoid se in formal writing; use hän there.

Use the negative verb and switch the object to partitive:

• En tilaa hänelle taksia nyt. = “I’m not ordering him/her a taxi now.”
  Pattern: en/et/ei… + verb stem (tilaa) + partitive object (taksia).

Finnish has no articles; context and endings do the work.

• Tilaan taksin. usually means “I’ll order a taxi.”
• To stress “one,” say yhden: Tilaan yhden taksin.
• To make it definite, specify: Tilaan sen taksin (“that taxi”) or Tilaan tutun/tietyn taksin (“a familiar/certain taxi”).

Use a numeral; after numbers ≥ 2, the noun is in partitive singular:

• Tilaan kaksi taksia. = “I’ll order two taxis.”
  For an indefinite plural (some taxis), use plural partitive: Tilaan takseja.

It’s a type 4 verb. In 1st person singular present: drop -ta and add the ending; with many -ata verbs, the preceding a lengthens:

• tilata → tilaan, pelata → pelaan
  But some -Vta verbs behave differently (e.g., haluta → haluan), so learn common patterns.

Yes.

• Past: (Minä) tilasin taksin hänelle (nyt).
  You usually drop nyt in the past unless you truly mean “just now” (then use äsken/juuri äsken): Tilasin hänelle taksin äsken.