وقتی داشتم با جاروبرقی کار میکردم، همسایه ما به بالکن آمد و سلام کرد.

This is the past progressive pattern in Persian:

• داشتم = I was / I had
• می‌کردم = I was doing

Together, داشتم کار می‌کردم means I was working / I was in the middle of working.

Persian can often express an ongoing past action with just می‌کردم, so وقتی با جاروبرقی کار می‌کردم is also possible. Adding داشتم makes the ongoing nature more explicit, like I was just in the middle of it when....

وقتی means when and introduces a time clause.

So:

• وقتی داشتم با جاروبرقی کار می‌کردم = When I was working with the vacuum cleaner

It sets the background for the main events that follow:

• همسایه ما به بالکن آمد و سلام کرد

A very common Persian pattern is:

• وقتی + past ongoing action, main event happened

That is exactly what this sentence is doing.

It is understandable and natural enough, but it is slightly more literal as I was working with the vacuum cleaner or I was using the vacuum cleaner.

A more idiomatic way to say I was vacuuming is often:

• داشتم جاروبرقی می‌کشیدم

That said, با جاروبرقی کار کردن is perfectly clear and emphasizes using or operating the appliance.

Here با means with.

So:

• با جاروبرقی = with the vacuum cleaner

In context, it has the sense of using the vacuum cleaner as an instrument. Persian often uses با this way to show the tool or means by which something is done.

Standard Persian spelling uses a half-space in forms like this:

• می‌کردم

The prefix می‌ attaches to the verb stem with a half-space, not a full space. In informal typing, people often write it less carefully, for example:

• میکردم
• می کردم

But the standard written form is:

• می‌کردم

The same applies in کار می‌کردم.

Both are possible.

• همسایه ما = our neighbor
• همسایه‌مان = our neighbor

The first is a more separate, analytic form using ما. The second uses the enclitic -مان, which also means our.

There is also an ezafe pronunciation here, so همسایه ما is pronounced like:

• همسایهِ ما / همسایه‌ی ما

In careful writing, you may also see:

• همسایهٔ ما
• همسایه‌ی ما

So this is normal Persian possessive structure.

Because Persian usually uses به with verbs of motion to mean to or toward a place.

So:

• به بالکن آمد = came to the balcony / came onto the balcony

Without به, the phrase would sound incomplete or ungrammatical in standard Persian.

They are the same verb, but in different registers:

• آمد = more formal or standard written form
• اومد = colloquial spoken form

So in everyday speech, many people would say:

• همسایه‌مون به بالکن اومد و سلام کرد

But in more standard writing, آمد is preferred.

Literally, it is something like did a greeting.

This is a very common Persian light verb construction:

• سلام = greeting / hello
• کرد = did

Together, سلام کرد means:

• said hello
• greeted

Persian often uses a noun plus کردن to make verbs. This is one of the most common patterns in the language.

Yes. Both are common:

• سلام کرد
• سلام گفت

Both can mean said hello.

A small nuance is that سلام گفت can feel a bit more directly like said hello, while سلام کرد can feel slightly more like greeted, but in many everyday contexts they overlap.

Because Persian can omit it when it is obvious from context.

If you want to make it explicit, you could say:

• به من سلام کرد = he/she said hello to me

So the full idea could be:

• همسایه ما به بالکن آمد و به من سلام کرد

But if the listener already understands that the greeting was directed at the speaker, Persian often leaves it out.

Yes, exactly.

That is one of the main things the grammar is showing:

• داشتم با جاروبرقی کار می‌کردم = ongoing background action
• همسایه ما به بالکن آمد و سلام کرد = shorter completed actions that happened during that time

So the structure is very similar to English:

• When I was vacuuming, our neighbor came to the balcony and said hello.

This is a very common storytelling pattern in Persian.