Learn Hardcore Chinese: nǐ juéde zhèyàng ānpái zěnmeyàng?

With 的: 这样的安排 clearly means “this kind of arrangement” (noun phrase). It’s a bit more explicit/formal.
Without 的: 这样安排 is very common in speech and can be understood as either “this arrangement” (NP) or “to arrange it like this” (VP). The sentence is natural either way.

Is 安排 a noun or a verb here?

It can be read both ways:

Noun: “this arrangement.”
Verb phrase: “arranging it like this.” Because it sits before 怎么样, both readings are fine. Adding 的 (这样的安排) pushes it toward the noun reading.

Why isn’t there a 吗 at the end?

怎么样 already makes it a question (“how is it/what do you think”). Adding 吗 would be redundant or ungrammatical. Don’t say “怎么样吗”.

What’s the difference between 怎么样 and 怎么?

怎么样 = “how is it / what do you think (of it)?” It asks for evaluation/opinion.
怎么 = “how / in what way?” It asks for method.
Compare:
这样安排怎么样？ “How is arranging it like this?”
怎么安排？ “How should we arrange it?”

How does 觉得 (juéde) compare with 想, 认为, 感觉, 以为?

觉得: “to feel/think” (most common for opinions; neutral and natural).
想: “to think/want”; in this context it can mean “think,” but it’s less idiomatic for asking opinions.
认为: “to deem/hold that”; more formal, often used in written/speechmaking contexts.
感觉: “to feel/sense”; more about subjective feeling; can overlap with 觉得 in casual speech.
以为: “to think (but be mistaken)”; don’t use it to ask for someone’s opinion.

What’s the nuance of 这样 vs 这么 (and 那样) here?

这样: “like this / in this way” (neutral; common in both speech and writing).
这么: very common in speech; often emphasizes degree/this manner close to the speaker; interchangeable here: 你觉得这么安排怎么样？
那样: “like that / in that way,” referring to something farther away or previously mentioned: 你觉得那样安排怎么样？

Can I use 这样子?

Yes, 这样子 is a colloquial variant: 你觉得这样子安排怎么样？ It’s more informal/regional in feel but widely understood.

How else could I phrase the same idea?

你觉得这个安排怎么样？ (points to a specific arrangement/plan)
我们这样安排，行吗/可以吗？ (asks workability/permission)
你怎么看这个安排？ (more direct: “What’s your take?”)
您看这样安排是否合适？ (politer/formal: “Would this arrangement be appropriate?”)
这样安排如何？ (concise, somewhat formal)

How do I answer this naturally?

Positive: 可以/行/挺好/很好/没问题/合适。
Neutral/soft: 还行/还可以/都可以/看你/问题不大。
Negative (softened): 不太合适/有点儿紧/可能不太方便。
Suggesting an alternative: 要不我们改成……？/是不是可以晚一点？/我建议……

How do I make it more polite?

Use 您: 您觉得这样安排怎么样？
Add softeners: 您觉得这样安排怎么样呢？ (gentler), 您看这样安排行不行？
More formal: 您看这样安排是否合适？/ 方不方便？

Is the word order fixed? Could I say “你觉得怎么样这样安排”?

Keep the thing being evaluated right before 怎么样: 你觉得 + [这样安排] + 怎么样？
“你觉得怎么样这样安排” is unnatural.

Pronunciation tips for tricky parts?

觉得: juéde — the de is neutral tone (not dé).
这样: zhèyàng — 4th tone + 4th tone.
怎么样: zěnme yàng — 3rd tone + neutral + 4th.
Speak zěnme smoothly with a light neutral me.

Can I replace 怎么样 with 怎样 or 如何?

Yes:

怎样 is a bit more formal/literary but fine: 你觉得这样安排怎样？
如何 is formal: 你觉得这样安排如何？

Do I need a measure word with 安排?

Not in this sentence. If you count or specify one arrangement, use 个: 一个安排/这个安排. If you mean the manner rather than a countable plan, no measure word is needed.

Can I drop 安排 and just say 你觉得这样怎么样？?

Yes, if the context makes “this (plan/way)” clear. Without 安排, it’s broader and relies on shared context to know what “this” refers to.

What’s the difference between ending with 吧 and 怎么样?

……吧？ (with a question mark) sounds like a tentative suggestion seeking confirmation: 我们这样安排吧？ (“Shall we arrange it like this?”).
……怎么样？ asks for an evaluation/opinion without directly proposing to finalize it.