بطاقة الغرفة معي.

Yes. In Arabic, the present-tense verb to be is usually not said.

So the sentence is a nominal sentence:

• بطاقة الغرفة = the room card
• معي = with me

Literally, it is something like The room card with me, which in natural English becomes The room card is with me or I have the room card.

معي means with me.

It is made of:

• مع = with
• ـي = me / my as a suffix

So:

• معي = with me
• معك = with you
• معه = with him

In everyday Arabic, with me often also implies possession, especially something you physically have on you or in your possession right now.

Arabic often expresses possession without using a direct verb like English have.

Instead, it uses expressions like:

• معي = with me
• عندي = at me / I have

So بطاقة الغرفة معي literally means The room card is with me, but the natural English meaning can be I have the room card.

Because Arabic commonly uses a structure called iḍāfa (the construct phrase).

In English, you might say:

• the card of the room
• or more naturally, the room card

In Arabic, this is expressed by simply placing two nouns together:

• بطاقة الغرفة

So there is no separate word for of here. The relationship is built into the noun phrase itself.

الغرفة means the room.

In an iḍāfa phrase, the second noun often carries the definiteness. So:

• غرفة = a room
• الغرفة = the room

Because the second noun is definite, the whole phrase بطاقة الغرفة becomes definite too:

• بطاقة الغرفة = the room card / the card of the room

In Levantine, a common pronunciation is something like bṭāʔet il-ghurfe or bṭāʔit il-ghurfe, depending on the region.

The important point is this:

The final ة in بطاقة is often pronounced like -t when the word is connected to another noun in an iḍāfa phrase.

So:

• on its own: بطاقة may sound more like bṭāʔa
• before another noun: بطاقة الغرفة becomes more like bṭāʔet il-ghurfe

That t sound is very normal here.

Because بطاقة by itself just means card.

If you wanted to say my card, you would say:

• بطاقتي

But this sentence is not saying my room card. It is saying:

• The room card is with me
• or I have the room card

So the possession belongs to the whole situation, expressed by معي, not by attaching my to بطاقة.

Yes, you could, and both are natural.

The difference is roughly:

• معي often emphasizes it is with me / on me / in my possession right now
• عندي often means I have in a more general sense

So if someone asks whether you physically have the card on you, معي is especially fitting.

Yes. You can also say:

• معي بطاقة الغرفة

Both are possible, but the emphasis changes a little.

• بطاقة الغرفة معي puts the room card first, as the topic
• معي بطاقة الغرفة starts with with me / I have, which can feel more like an answer to Who has the room card?

Both are understandable and natural in context.

It would also be understood in Standard Arabic.

The structure itself is not uniquely Levantine:

• بطاقة الغرفة معي

What changes most in Levantine is the pronunciation, especially things like:

• the sound of ة
• the pronunciation of ال
• everyday rhythm and vowels

So grammatically, the sentence is broadly understandable, while the spoken pronunciation is what makes it sound specifically Levantine.