Learn Hardcore Chinese: nǐ hé tā de xiǎngfǎ yíyàng.

As a shortcut for:
你的想法和她的想法一样
(Your ideas and her ideas are the same.)
Here, 的 is written only once (after 她) to avoid repetition, but it is understood for both.
As:
你和她的想法一样
where 你和她的 = you and her (both) ‘s, and 想法 = idea(s)
So: The ideas of you two are the same.

In either case, 的 is needed to link 她 to 想法; Chinese allows you to share that 的 + noun with both people, so you don’t have to write 的 twice.

2. Can I leave out 的 and say 你和她想法一样?

Yes, you can, and native speakers often do, especially in spoken Chinese.

你和她的想法一样
Subject = 你和她的想法 (your and her ideas)
Predicate = 一样 (are the same)
你和她想法一样
Subject = 你和她 (you and she)
Predicate = 想法一样 ([your] ideas are the same)

The meaning in practice is the same. With 的, it feels a bit more explicit or careful; without 的, a bit more colloquial and compact. Both are natural.

3. What is the role of 和 (hé) here? Does it mean and or with? Could I use 跟?

In this sentence, 和 is linking two people for comparison:

你和她的想法一样
= Your ideas and her ideas are the same
(or: Your thinking is the same as hers)

Here 和 plays the role of and (also conceptually close to with: you and she (together) …).

You can almost always replace 和 with 跟 in this kind of structure:

你跟她的想法一样。

They mean the same.
Nuance: 跟 sounds a bit more colloquial and is especially common when you mean with in the sense of interaction, but here both are fine.

4. Where is the verb to be? Why don’t we need 是?

Chinese often uses an adjective directly as a predicate without 是:

你很忙。 – You are busy.
这个菜好吃。 – This dish is tasty.

In 你和她的想法一样:

Subject: 你和她的想法 – your and her ideas
Predicate: 一样 – [are] the same

There is no separate word like are; 一样 itself functions as the predicate.

You can also say:

你和她的想法是一样的。

This is also correct and quite natural. The version with 是 … 的 sounds a bit more formal or emphatic; the short version without 是 is simpler and very common in speech.

5. What exactly does 一样 (yíyàng) mean, and what part of speech is it?

一样 means the same, identical, or of the same kind.

In this sentence it functions like a predicate adjective:

A 的 B 一样
→ A’s B [is] the same.

Other common patterns with 一样:

跟 / 和 + somebody + 一样
我跟你一样高。 – I’m as tall as you / the same height as you.
跟 / 和 + something + 一样 + Adj
这个跟那个一样贵。 – This is as expensive as that.

So 一样 here is not a verb but a descriptive word that acts like the verb to be the same.

6. What is the difference between 想法, 想, and 觉得?

They’re related but not interchangeable:

想法 (xiǎngfǎ)
A noun: idea, way of thinking, viewpoint.
- 他的想法很有意思。 – His ideas are very interesting.
想 (xiǎng)
A verb meaning:
- to think, to consider
- to want, to intend
  e.g. 我想去中国。 – I want to go to China.
觉得 (juéde)
A verb meaning:
- to feel, to think (expressing an opinion)
  e.g. 我觉得这个不太好。 – I think this is not so good.

In 你和她的想法一样, we are comparing ideas / ways of thinking, so the noun 想法 is needed, not the verbs 想 or 觉得.

You could make a different but related sentence:

你跟她想的一样。 – You think the same (way) as she does.

Here 想的 turns the verb 想 into something like the way [you] think.

7. Can I say 你的想法和她的一样 instead? Is there any difference?

Yes, that is also completely correct:

你的想法和她的一样。

Here:

你的想法 = your ideas
她的 = hers (her ideas, understood)
一样 = are the same

This version is a bit more symmetrical and may feel a little clearer to beginners, because it mirrors the English structure Your ideas are the same as hers.

Meaning-wise, 你的想法和她的一样 and 你和她的想法一样 are essentially the same in everyday use.

8. How would I negate this sentence or turn it into a question?

Very simple patterns:

Yes–no question: add 吗 at the end
- 你和她的想法一样吗？
  Are your ideas the same as hers?
Negative: put 不 before 一样
- 你和她的想法不一样。
  Your ideas are not the same as hers.

You can combine both:

你和她的想法是不是一样？
(literally: Are or are not your ideas the same?)
This also asks a yes–no question, with a slightly more inquisitive tone.

9. Is 想法 singular or plural here? Does Chinese mark idea vs ideas?

Chinese nouns usually do not mark singular vs plural the way English does. 想法 by itself can mean idea or ideas, depending on context.

他有一个想法。 – He has an idea.
他们的想法很多。 – Their ideas are many / They have many ideas.

In 你和她的想法一样, it’s best to understand it as your way(s) of thinking are the same. Whether you think of it as singular or plural in English doesn’t change the Chinese.

10. Why is 一样 pronounced yíyàng, not yīyàng?

This is a case of tone sandhi for 一 (yī).

Rule (main one you need here):

When 一 (yī, 1st tone) is followed by a 4th tone syllable, 一 changes to 2nd tone (yí).

Since 样 (yàng) is 4th tone, 一 becomes yí:

一 + 样 (yàng) → yíyàng (一样)

So the correct pronunciation is yíyàng, even though dictionaries list 一 in 1st tone in isolation.

11. 他 (he) and 她 (she) sound the same in Mandarin. In speech, how do people know which one is meant?

You’re right: 他, 她, and even 它 (it) are all pronounced tā.

In spoken Chinese, people rely on context to know whether tā refers to he, she, it, or they.

In writing, the characters disambiguate:

他 – he / him (male, or generic person)
她 – she / her (female, specifically)
它 – it (things, animals, abstract)

In your sentence, 你和她的想法一样, you only know it’s she because the character 她 is used. If someone just said it aloud, 你和他/她的想法一样, you’d figure out the gender from context or not worry about it at all.

12. Are there other natural ways to express the same idea in Chinese?

Yes, several. All of these are natural, with slightly different focuses:

你跟她想的一样。
– You think the same (way) as she does.
你的想法跟她的一样。
– Your ideas are the same as hers.
你和她有一样的想法。
– You and she have the same idea(s).
你和她的看法一样。
– Your views/opinions are the same.
(Using 看法 = viewpoint, opinion)

All of them convey the core idea that your way of thinking matches hers.