احنا عايزين نتبنى قطة.

A natural word-for-word breakdown is:

• احنا = we
• عايزين = wanting / want (plural form used with we)
• نتبنى = adopt / literally we adopt
• قطة = a cat

So the structure is roughly:

• we + want + adopt + a cat

More literally, Arabic is doing something like we are wanting [that] we adopt a cat, but in normal English that just becomes We want to adopt a cat.

احنا is Egyptian Arabic, while نحن is Modern Standard Arabic.

So:

• احنا / إحنا = Egyptian Arabic we
• نحن = Standard Arabic we

A native Egyptian speaker would normally say احنا or إحنا in everyday speech.
If you wanted the Standard Arabic version of the whole sentence, it would be something like:

• نحن نريد أن نتبنّى قطةً

So this sentence is clearly colloquial Egyptian, not MSA.

In Egyptian Arabic, عايز is one of the most common ways to say want.

Its forms are:

• عايز = I want / he wants, depending on context and subject
• عايزة = female singular
• عايزين = plural, including we

So احنا عايزين means we want.

Grammatically, عايز originally comes from a participle, but for learners it's best to think of it as the normal everyday Egyptian way to say want.

Because Egyptian Arabic usually does not use a separate word like English to in this pattern.

In English:

• We want to adopt a cat

In Egyptian Arabic:

• احنا عايزين نتبنى قطة

The pattern is:

• عايز / عايزة / عايزين + present-tense verb

So:

• عايزين نتبنى = want to adopt

In very formal Standard Arabic, you often see أن before the next verb, but in everyday Egyptian that is usually left out.

Because Arabic does not use an infinitive the same way English does.

English says:

• to adopt

Egyptian Arabic instead uses a conjugated present verb:

• نتبنى

The نـ at the beginning marks we, so نتبنى literally means we adopt. But after عايزين, it gives the meaning to adopt:

• عايزين نتبنى = we want to adopt

So even though it looks like a present-tense verb, in this structure it corresponds to English to + verb.

Yes. With احنا meaning we, عايزين is the normal everyday form.

So:

• احنا عايزين = we want

This is the usual form regardless of whether the group is male, female, or mixed.

For singular, you do see gender clearly:

• أنا عايز = I want (male speaker)
• أنا عايزة = I want (female speaker)

But with we, Egyptian Arabic normally uses عايزين.

You can often leave it out.

Arabic often drops subject pronouns when the meaning is already clear. So both of these are natural:

• احنا عايزين نتبنى قطة
• عايزين نتبنى قطة

The version with احنا is a bit more explicit or emphatic.
The version without it is also very normal in conversation.

A helpful pronunciation is:

• eḥna ʿāyzeen nitbanna ʔoṭṭa

A simpler learner-style version would be:

• ehna 3ayzeen netbanna oTTa

A few useful notes:

• احنا sounds like ehna
• عايزين sounds roughly like 3ayzeen
• نتبنى sounds roughly like netbanna
• قطة in Egyptian is usually pronounced ʔoṭṭa or simply otta

Also, in Cairene Egyptian, ق is often pronounced as a glottal stop, not a hard q sound.
And the طّ in قطة is doubled, so you hold that consonant slightly: oṭ-ṭa.

Literally, قطة is the feminine form, and it can specifically mean a female cat.

But in everyday Egyptian speech, قطة is also very commonly used just to mean a cat in general.

If you specifically want to say a male cat, you can use:

• قط

So in this sentence, learners should understand قطة simply as a cat.

In Egyptian Arabic, case endings and tanween are usually not written or pronounced in normal speech.

So in MSA you might see:

• قطةً

But in Egyptian everyday usage, you simply get:

• قطة

That still means a cat.

If you want the cat, you add ال:

• القطة = the cat

In Egyptian pronunciation, that is often said something like:

• el-ʔoṭṭa

The natural Egyptian negative is:

• احنا مش عايزين نتبنى قطة

This means:

• We don't want to adopt a cat

Here مش negates عايزين:

• عايزين = want
• مش عايزين = don't want

This is the normal everyday way to negate this kind of sentence in Egyptian Arabic.