Learn Hardcore Korean: hotel peureonteue chuga sugeoneul yocheonghaeyo. - I request extra towels at the hotel front desk.

에 marks the target/destination of your request: you’re directing the request to the front desk as an institution. Hence, 호텔 프런트에 요청해요 is natural.
에서 marks the location where the action happens: 호텔 프런트에서 요청해요 ≈ “I make the request at the front desk (that’s where I do it).”
에게/한테 is for a person/people: 프런트 직원에게(한테) 요청해요 = “I ask the front-desk staff.” All three are possible; choose based on whether you’re highlighting the recipient (에/에게/한테) or the physical location (에서). Using 에 here treats the front desk as the receiving body.

Does 요청해요 sound natural in a real hotel situation?

It’s correct but a bit formal/“business-like” for face-to-face speech. What you’ll hear most:

수건 좀 더 주세요.
수건 두 장만 더 주시겠어요?
수건 조금만 더 부탁드려도 될까요? Use 요청해요 in narration (e.g., telling someone what you’ll do) or in written/formal contexts. To the staff directly, 주세요/부탁드려요 is more natural.

Is 추가 수건 the most natural way to say “extra towels”?

It’s fine, but it sounds a bit written/formal. In everyday talk, people usually say:

수건을 더 or 수건 좀 더
여분의 수건 (“spare towels”) is also common. If you like the “additional” nuance, you can say 추가로 수건을. Hotels may also use 타월 (loanword) instead of 수건.

How do I specify how many towels I want?

Use the counter 장 for towels.

수건 두 장 더 주세요. (Please give me two more towels.)
큰 수건 한 장, 작은 수건 한 장 부탁드려요. (One big, one small.) Typical hotel terms: 바스타월 (bath towel), 페이스타월 (face towel).

Should I say 프런트에 or 프런트로?

프런트에 = to/at the front desk (target or location). Works with 요청하다.
프런트로 = toward the front desk (direction). Use when movement or a path is in focus:
- 프런트로 가서 요청할게요. (I’ll go to the front desk and ask.)
- 프런트로 전화해서… (Call to the front desk and…) Saying 프런트로 요청하다 is odd; prefer 프런트에 요청하다.

Can I change the word order?

Yes. Korean word order is flexible as long as particles are clear. For example:

추가 수건을 호텔 프런트에 요청해요.
호텔 프런트에 요청해요, 추가 수건을. (more topical/emphatic) Keep the verb at the end and make sure particles (에/을) stay attached to the right nouns.

Can I drop the object particle 을?

Often yes in casual speech:

호텔 프런트에 추가 수건 요청해요.
But with a formal verb like 요청하다, keeping 을 sounds cleaner: 추가 수건을 요청해요. With more natural spoken phrasing, particles are often dropped: 수건 좀 더(를) 주세요.

What level of politeness is this, and how can I make it more/less polite?

Current sentence (요청해요) is polite neutral (해요체).
More polite/formal (for calls, notes): 호텔 프런트에 추가 수건을 요청합니다., or more natural: 수건 추가 부탁드립니다.
Very polite ask to staff: 수건 두 장만 더 주실 수 있을까요?
Casual (to a friend/roommate): 프런트에 수건 더 요청해. Adding softeners like 좀, 혹시, 실례하지만 increases politeness.

What’s the difference between 요청하다, 부탁하다, 신청하다, and 주문하다?

요청하다: request (formal/institutional). Neutral but a bit stiff in speech.
부탁하다: ask a favor (most natural to people in service situations).
- Polite: 부탁드려요 / 부탁드립니다.
신청하다: apply/register for something (a service/event). Not for towels.
주문하다: order items (food, products). Not usually for free hotel towels. To front-desk staff, prefer 주세요 or 부탁드려요 over 요청해요.

Any pronunciation tips for this sentence?

호텔: [호텔] ho-tel
프런트에: [프런트에] peu-reon-te-e
추가: [추가] chu-ga
수건을: resyllabifies to [수거늘] su-geo-neul
요청해요: [요청해요] yo-cheong-hae-yo
Linking especially happens in 수건을 → the final ㄴ moves to the next syllable.

Is it okay to say 프론트 instead of 프런트?

You’ll see and hear both. The standard spelling is 프런트. 프론트 appears on signs or colloquially, but for writing or study, stick with 프런트.

Why is there no subject like “I” in the sentence?

Korean often drops obvious subjects. Here, “I” is understood from context. You can add it for emphasis:

How would I say this on the phone or in a chat to the front desk?

Phone: 안녕하세요. 000호실인데요. 수건 두 장만 더 주실 수 있을까요?
Chat: 안녕하세요, 000호실입니다. 수건 두 장 추가 부탁드립니다.
Adding room number early is standard and sounds professional.