من هنوز بلیت قطار را پیدا نکرده ام، اما یادم هست که آن را در چمدان گذاشتم.

Yes. In Persian, subject pronouns are often omitted because the verb ending already shows the person.

Here, کرده‌ام means I have done / I have ..., so من is not strictly necessary. The sentence could still be correct without it:

هنوز بلیت قطار را پیدا نکرده‌ام...

Including من adds a little emphasis or clarity, especially in careful or written style.

هنوز means still or yet, depending on the sentence.

In this sentence, because the verb is negative, it corresponds to English yet:

من هنوز بلیت قطار را پیدا نکرده‌ام
= I still haven’t found the train ticket / I haven’t found the train ticket yet

Its position before the object and verb is very normal in Persian. It often appears before the part of the sentence it modifies, especially before the verb phrase.

بلیت means ticket and قطار means train. Together, بلیت قطار literally means ticket of train, but in natural English we say train ticket.

This is a very common Persian noun combination: one noun modifies another without needing a special word in between.

So:

• بلیت قطار = train ticket
• درِ خانه would use ezafe or another marker in a different structure, but here simple noun + noun is enough

Learners often expect something like ticket of the train, but Persian commonly uses compact noun combinations like this.

را marks the direct object, especially when it is specific or definite.

So in:

بلیت قطار را پیدا نکرده‌ام

the thing being found is بلیت قطار, and را marks it as the object.

A helpful way to think of it is:

• را often appears with the, this, that, my, etc. in English
• it usually signals that the speaker has a particular item in mind

That is why it also appears later in آن را.

For the same reason: آن is the direct object of گذاشتم.

So:

آن را در چمدان گذاشتم
= I put it in the suitcase

Here:

• آن = that / it
• را = direct object marker

Together, آن را means it or that as the object of the verb.

This is the negative present perfect form of the compound verb پیدا کردن = to find.

Breakdown:

• پیدا کردن = to find
• کرده‌ام = I have done
• نکرده‌ام = I have not done

So:

پیدا نکرده‌ام
literally = have not found

This is a compound verb, which is very common in Persian. The non-verbal element is پیدا, and the verbal element is a form of کردن.

In modern Persian spelling, you may see both styles, but the more standard modern written form often uses a half-space:

• نکرده‌ام
• کرده‌ام

In less careful typing, people may write:

• نکرده ام
• کرده ام

So the sentence you saw is normal, but many textbooks and edited texts prefer the half-space version.

Grammatically, it is the past participle plus the auxiliary ام.

Because the speaker is talking about a present situation resulting from a past search:

I still haven’t found the ticket.

That is exactly the kind of meaning the present perfect often gives in Persian too.

Compare:

• پیدا نکرده‌ام = I haven’t found
• پیدا نکردم = I didn’t find

The second one sounds more like a completed past event. The first one connects the past to the present state.

اما means but or however.

It connects the two clauses:

• I still haven’t found the train ticket
• but I remember that I put it in the suitcase

It is a standard written and spoken conjunction.

Literally, یادم هست means something like my memory is or it is in my memory, but naturally it means:

I remember

Breakdown:

• یاد = memory, recollection
• ـم = my
• هست = is

So Persian often expresses remembering with this structure rather than using a simple verb exactly like English remember.

Because Persian often uses idiomatic expressions where English uses a single verb.

A very common pattern is:

• یادم هست = I remember
• یادم نیست = I don’t remember

There is also the verb به یاد داشتن, but in everyday Persian, expressions with یاد are extremely common and natural.

So this sentence uses a very normal Persian way to say I remember.

که here means that and introduces the content of what the speaker remembers.

So:

یادم هست که آن را در چمدان گذاشتم
= I remember that I put it in the suitcase

In Persian, که is very commonly used to connect clauses like this. In some contexts it can be omitted, but keeping it is very natural and clear.

آن literally means that, but it can also function as it, especially in more formal or written Persian.

So:

آن را در چمدان گذاشتم
can mean
I put it in the suitcase

In more conversational Persian, many speakers would say:

اون رو در چمدان گذاشتم

where:

• اون = spoken form of آن
• رو = spoken form of را

So the sentence you have is more standard/written in style.

Because او is used for he/she and sometimes for people in a formal sense, not for objects like a ticket.

For non-human things, Persian uses آن or این, or in speech اون or اینو/اونو depending on the structure.

Since the ticket is an object, آن را is correct.

در means in / inside, and چمدان means suitcase.

So:

در چمدان = in the suitcase

Persian does not have articles like a and the in the same way English does, so whether you translate it as in a suitcase or in the suitcase depends on context. Here, because the speaker clearly has a particular suitcase in mind, English naturally uses the suitcase.

Because Persian is generally a verb-final language. The basic order is often:

subject + object + other elements + verb

So:

آن را در چمدان گذاشتم
literally follows the Persian order:
it + in the suitcase + put

This is completely normal in Persian.

Because the two parts describe different time relationships.

• پیدا نکرده‌ام describes the present situation: up to now, I have not found it.
• گذاشتم refers to a completed action in the past: I put it in the suitcase.

So the tense contrast is natural:

I still haven’t found it, but I remember that I put it in the suitcase.

The remembering is relevant now, but the putting happened at a specific earlier time.

It is fairly neutral to standard, and it leans a bit toward written or careful spoken Persian.

Features that make it more standard include:

• آن را instead of colloquial اون رو
• هست instead of a more reduced spoken form
• full, clear sentence structure

A colloquial version might look more like:

من هنوز بلیت قطار رو پیدا نکردم، اما یادمه که اون رو توی چمدون گذاشتم.

Both mean the same thing, but your original sentence is better for standard Persian study.

Yes, it can, but the tone changes a little.

For example:

به یاد دارم که آن را در چمدان گذاشتم

This also means I remember that I put it in the suitcase.

However:

• یادم هست is very common and natural
• به یاد دارم can sound a little more formal or literary in some contexts

So the original phrasing is very natural.

It has two main parts joined by اما:

1. من هنوز بلیت قطار را پیدا نکرده‌ام
   = I still haven’t found the train ticket

2. اما یادم هست که آن را در چمدان گذاشتم
   = but I remember that I put it in the suitcase

Inside the second part, که introduces a subordinate clause:

• main clause: یادم هست
• subordinate clause: آن را در چمدان گذاشتم

So the sentence is a good example of:

• object marking with را
• a compound verb
• present perfect vs. simple past
• a clause introduced by که