من خوشحال هستم، چون امروز بعد از کلاس به خانه میروم.

Not strictly.

Persian verbs usually show the subject clearly, so هستم already means I am and می‌روم already means I go / I am going. Because of that, you can often omit من:

خوشحال هستم، چون امروز بعد از کلاس به خانه می‌روم.

Adding من is still correct. It can make the sentence clearer, more explicit, or slightly more emphatic.

Because Persian often makes this kind of sentence with:

adjective + form of بودن / to be

So:

• خوشحال = happy
• هستم = I am

Together, خوشحال هستم means I am happy.

This is very normal Persian structure. English does the same idea, but Persian keeps the to be form at the end of the clause.

Yes, and that is often more natural.

خوشحالم is a shorter form of I am happy. In everyday Persian, attaching the -م ending to the predicate is very common.

So these are both correct:

• من خوشحال هستم
• من خوشحالم

The second one is usually more natural in speech. Your sentence is correct as written, but many native speakers would prefer من خوشحالم.

Because Persian usually puts the verb at or near the end of the clause.

That is different from English.

Compare:

• English: I am happy
• Persian: من خوشحال هستم

And:

• English: I go home
• Persian: به خانه می‌روم

So in your sentence, both هستم and می‌روم come at the end of their clauses, which is very typical Persian word order.

چون means because.

It introduces the reason:

• من خوشحال هستم = I am happy
• چون امروز بعد از کلاس به خانه می‌روم = because today after class I am going home

So the second clause explains the reason for the first one.

You can also reverse the order in Persian:

چون امروز بعد از کلاس به خانه می‌روم، خوشحالم.

That also means Because I’m going home after class today, I’m happy.

It means after class.

Breakdown:

• بعد = after
• از = from/of, but here it is part of the fixed expression
• کلاس = class

So بعد از کلاس is a common phrase meaning after class.

You can use the same pattern with other nouns too:

• بعد از کار = after work
• بعد از غذا = after food / after the meal

Because به often marks movement toward a place, like to in English.

So:

• به خانه می‌روم = I go to home / I go home

With verbs of motion, به is very common:

• به مدرسه می‌روم = I go to school
• به دانشگاه می‌روم = I go to university

In everyday speech, native speakers sometimes drop به in some expressions, but به خانه می‌روم is completely correct and standard.

Because Persian does not have a word exactly like English the.

A bare noun like خانه can mean:

• house
• the house
• home

The exact meaning depends on context.

In this sentence, خانه is naturally understood as home.

If you want to say my home / my house, you can say:

• خانه‌ام

If you want a house, you would often say:

• یک خانه

Formally, it is a present-form verb, but Persian often uses this form for a planned or near-future action.

So می‌روم can mean:

• I go
• I am going
• I will go

The context decides the best English translation.

Here, because of امروز بعد از کلاس (today after class), the meaning is naturally something like:

• I’m going home after class today
• I’ll go home after class today

So even though the form is present, the meaning can be future in context.

می- is a very important Persian verb prefix.

In forms like می‌روم, it usually marks an imperfective/present-type meaning. In practical learner terms, it is the part that helps make forms like:

• می‌روم = I go / I am going
• می‌روی = you go
• می‌رود = he/she goes

So in this sentence:

• روم is the verb part with the I ending
• می- helps create the normal present-style form

You do not usually translate می- as a separate word by itself.

They are the same word.

The more standard modern spelling is:

• می‌روم

This uses a half-space after می.

But many people type it without the half-space:

• میروم

That is very common in informal typing. The meaning and pronunciation are the same.

So if you see می‌روم and میروم, think of them as the same verb form.

Because رفتن is one of those Persian verbs whose present stem and past stem are different.

For this verb:

• infinitive: رفتن = to go
• past stem: رفت-
• present stem: رو-

So:

• رفتم = I went
• می‌روم = I go / I am going

This is normal Persian grammar, even though it can feel strange at first to English speakers.

A very natural spoken version would be:

من خوشحالم، چون امروز بعد از کلاس می‌رم خونه.

Changes:

• خوشحالم instead of خوشحال هستم
• می‌رم instead of می‌روم
• خونه instead of خانه

Your original sentence is correct and sounds more standard or careful. The spoken version sounds more casual and conversational.

A helpful pronunciation guide is:

man khosh-hâl hastam, chon emruz ba'd az kelâs be khâne mi-ravam

A few notes:

• خوشحال sounds like khosh-hâl
• خانه sounds like khâne
• می‌روم in careful speech is mi-ravam
• In everyday speech, می‌روم is often pronounced more like miram

So a casual spoken version may sound closer to:

man khoshhâlam, chon emruz ba'd az kelâs miram khoone