wǒ xiǎng qǐng tā lái wǒ jiā chīfàn.

A natural way to parse it is:

我想 / 请她 / 来我家 / 吃饭

• 我想 = I want / I’d like to
• 请她 = invite her
• 来我家 = to come to my home
• 吃饭 = to eat / have a meal

So the overall structure is:

subject + 想 + 请 + person + 来 + place + verb

In very natural English, it means something like:

I want to invite her to come to my place for a meal.

Chinese often strings actions together in sequence, so instead of using lots of extra words like to, for, or and, it simply places the actions one after another.

Yes, 想 here means want to or would like to.

So:

• 我想请她来我家吃饭 = I want to invite her to my home for a meal

Depending on context, 想 can sound:

• direct: want to
• softer/politer: would like to
• sometimes even am thinking of

So in conversation, this sentence can feel a bit softer than a very blunt English I want.

请 has several related meanings, and that often confuses learners.

Common uses include:

• please
  
  • 请坐 = Please sit
• invite
  
  • 请她来 = invite her to come
• treat someone to something
  
  • 请你吃饭 = treat you to a meal / invite you out to eat

In your sentence, 请 means invite.

So 请她来我家吃饭 is not please her come...
It means invite her to come to my home and eat.

Because in Chinese, the person being invited usually comes directly after 请.

Pattern:

请 + person + action

Examples:

• 请她来 = invite her to come
• 请你吃饭 = invite you to eat / treat you to a meal
• 请他们帮忙 = ask them to help

So 她 is the object of 请.

You can think of it as:

• 请她 = invite her
• 来我家吃饭 = to come to my home and eat

Chinese usually does not need little linking words in the same way English does.

In English, we say:

invite her to come to my house to eat

Chinese often just places the ideas in order:

请她 来 我家 吃饭

Literally, that is closer to:

invite her come my home eat

This is completely normal in Chinese. The relationships between the parts are understood from word order.

So even though there is no separate word for every English to, the meaning is clear.

Both are grammatically possible, but 我家 is much more natural here.

• 我家 = my home / my place
• 我的家 = literally my home, but it often sounds more emphasized, descriptive, or slightly less conversational in sentences like this

Chinese often omits 的 with close relationships or very common personal nouns, especially in everyday speech.

Examples:

• 我妈 = my mom
• 我朋友 = my friend
• 我家 = my home / my place

So in this sentence, 来我家吃饭 sounds very natural.

Historically, yes:

• 吃 = eat
• 饭 = rice / meal

But in modern everyday Chinese, 吃饭 usually means:

• eat a meal
• have a meal
• sometimes just eat

So here, 来我家吃饭 means:

• come to my house to eat
• more naturally: come over to my house for a meal

It does not mean they are necessarily eating only rice.

Because the action is toward the speaker’s location.

• 来 = come toward the speaker
• 去 = go away from the speaker

Since the place is 我家 (my home), the speaker sees it as movement toward them, so 来 is natural:

• 来我家 = come to my house

If the speaker were talking about another location not centered on themselves, 去 might be used instead.

Because 我家 here is the destination of 来, not just a location phrase standing by itself.

• 来我家 = come to my house

You do not need 在 after verbs of movement like 来 and 去 when naming the destination.

Compare:

• 她在我家吃饭。 = She is eating at my house.
  Here 在 marks location.
• 她来我家吃饭。 = She comes to my house to eat.
  Here 我家 is the destination after 来.

So 来我家 is correct and natural.

Usually, yes, or at least it strongly suggests that you are the host.

When 请 is used with eating, it often carries the idea of:

• invite someone for a meal
• host them
• sometimes treat them

So 我想请她来我家吃饭 sounds like:

I’d like to invite her over to my place for a meal
with the implication that you are hosting.

At someone’s home, that hosting meaning is especially natural.

Yes, it is natural and correct.

It sounds like something a real speaker might say.

A few very similar natural variations are:

• 我想请她来我家吃个饭。
  Slightly conversational; 吃个饭 sounds very natural in speech.
• 我想请她到我家吃饭。
  Also natural; 到我家 instead of 来我家
• 我想请她来家里吃饭。
  家里 = at home / to my place, also very common

Your original sentence is perfectly good.

Yes, you can replace 她 with 他 if you mean him.

• 她 = she / her
• 他 = he / him

But in spoken Mandarin, they are pronounced the same:

• 她 = tā
• 他 = tā

So when speaking, you usually know which one is meant from context. The difference is visible mainly in writing.

Not very well. A word-for-word gloss would be something like:

I / want / invite / her / come / my home / eat meal

That helps show the structure, but it is not good English.

A natural English translation would be:

• I want to invite her to my house for dinner.
• I’d like to invite her over to my place for a meal.

This is a good example of how Chinese often uses simple word order rather than many connecting words.