اشتريت دوا جديد من الصيدلية، ورح اخده بعد الفطور.

Because the verb already tells you who the subject is. In اشتريت, the ending -ت shows I bought, so أنا is not necessary.

You can add أنا for emphasis or contrast, but in normal speech it is often omitted:

• اشتريت دوا جديد = I bought new medicine
• أنا اشتريت دوا جديد، مو هو = I bought new medicine, not him

اشتريت is the past tense verb I bought.

It comes from the verb اشترى / يشتري = to buy. In Levantine, as in many other varieties of Arabic, the -ت ending marks first person singular in the past:

• اشتريت = I bought
• اشتريتِ = you bought (to a woman, usually distinguished in speech more than in casual writing)
• اشترى = he bought

So here اشتريت is doing all the work of I bought by itself.

دوا is the common colloquial Levantine form of دواء.

A native speaker in everyday conversation is much more likely to say دوا than the more formal دواء. They mean the same thing, but:

• دوا = everyday Levantine
• دواء = more formal / MSA-like

So this is a very normal dialect choice.

Because in Arabic, adjectives normally come after the noun they describe.

So:

• دوا جديد = new medicine
• literally: medicine new

This is the normal word order in Levantine and in MSA too.

Because دوا is treated as a masculine singular noun, so the adjective has to match it.

Arabic adjectives agree with the noun in gender and number. Since دوا is masculine singular, the adjective is also masculine singular:

• دوا جديد = new medicine

If the noun were feminine, the adjective would usually be feminine too.

Because there is no ال- on the noun or the adjective.

In Arabic:

• دوا جديد = a new medicine
• الدوا الجديد = the new medicine

In Levantine, indefiniteness is usually just shown by the absence of ال-. You do not need a separate word for a/an.

Yes, من صيدلية is possible, but من الصيدلية is very natural if the speaker means from the pharmacy in a specific or understood sense.

Arabic often uses the definite article in places where English may be more flexible. In this sentence, من الصيدلية sounds very normal.

So:

• من الصيدلية = from the pharmacy
• من صيدلية = from a pharmacy

Both are grammatical, but the version with ال- is very common in everyday speech.

The ل of ال- is not pronounced normally here, because ص is a sun letter.

So الصيدلية is pronounced roughly like is-saydaliyye or es-saydaliyye, not al-saydaliyye.

A useful rule:

• with sun letters, ال- assimilates to the next consonant
• the spelling stays the same, but the pronunciation changes

So in speech, you hear something like a doubled s/ṣ sound.

رح is a very common Levantine future marker. It means something like will or going to.

So:

• رح اخده = I will take it

This is one of the most useful future markers in Levantine. Depending on the region, you may also hear حـ used in similar ways.

The -ه is an attached object pronoun meaning it or him. Here it refers to دوا, so it means it.

So اخده is basically:

• آخد / اخد = I take
• -ه = it

Together: I take it / I will take it, depending on context. In this sentence, because of رح, it means I will take it.

In Levantine pronunciation, this ending is often heard as -o, so اخده is commonly pronounced something like aakhdo.

Because after رح, Levantine normally uses the verb without the habitual/present prefix بـ-.

Compare:

• باخده = I take it / I usually take it / I am taking it
• رح اخده = I will take it

So رح already marks the future, and the بـ- is usually dropped.

بعد means after, and here it is followed by a noun phrase:

• بعد الفطور = after breakfast

Arabic very often uses ال- with meals, times, and other familiar nouns even when English would not say the. So الفطور here is completely natural.

You can also express the idea with a clause:

• بعد ما افطر = after I eat breakfast

But بعد الفطور is shorter and very common.

Yes, فطور is a very common Levantine word for breakfast.

Learners may also see إفطار, but in everyday Levantine فطور is extremely common for the morning meal. In some contexts إفطار can sound more formal or can refer specifically to breaking a fast, especially in Ramadan-related contexts.

So for ordinary daily speech, فطور is a very useful word to know.

A more MSA-style version would be:

اشتريت دواءً جديدًا من الصيدلية، وسآخذه بعد الفطور.

Key differences:

• دوا becomes دواء
• رح becomes a more formal future form like سـ
• اخده becomes آخذه
• MSA has case endings in full formal grammar, though they are often not written in everyday unvowelled text

So the original sentence is clearly everyday Levantine, not formal MSA.