Tansiyonum düşük, ben biraz su içiyorum.

In Turkish, the verb to be is usually not expressed in the 3rd person present tense.

So:

• Tansiyonum düşük = My blood pressure is low
• literally: my-blood-pressure low

This is very normal Turkish. In the present tense, Turkish often just puts the subject and the predicate next to each other.

Compare:

• Hava soğuk. = The weather is cold.
• Ev büyük. = The house is big.

So düşük works as the predicate, and is is simply understood.

The ending -um means my.

So:

• tansiyon = blood pressure
• tansiyonum = my blood pressure

This is the 1st person singular possessive suffix.

A few similar examples:

• ev = house → evim = my house
• arabam = my car
• suyum = my water

The exact form of the possessive ending changes because of vowel harmony:

• -ım / -im / -um / -üm

Here it becomes -um, so tansiyonum.

Because here düşük is not directly describing the noun inside a noun phrase; it is the predicate of the sentence.

Compare these two patterns:

• düşük tansiyon = low blood pressure
  
  • adjective + noun
• tansiyonum düşük = my blood pressure is low
  
  • noun + predicate adjective

So:

• before the noun: describing
• after the noun: stating what it is

This is a very common distinction in Turkish.

Usually, no.

Turkish verbs already show the subject, so içiyorum already means I am drinking.

That means these are both possible:

• Ben biraz su içiyorum.
• Biraz su içiyorum.

The version with ben adds emphasis, contrast, or just makes the subject more explicit.

For example, ben may sound like:

• I’m drinking some water
• As for me, I’m drinking some water
• I am drinking some water

In many everyday situations, native speakers would simply say:

• Tansiyonum düşük, biraz su içiyorum.

İçiyorum comes from the verb içmek = to drink.

It breaks down like this:

• iç- = verb stem
• -iyor = present continuous marker
• -um = I

So:

• içiyorum = I am drinking

A few similar forms:

• geliyorum = I am coming
• gidiyorum = I am going
• yapıyorum = I am doing

This tense is very commonly used for actions happening right now.

Because su here is a non-specific / indefinite direct object.

In Turkish, a direct object often takes the accusative ending only when it is specific or definite.

So:

• Biraz su içiyorum. = I’m drinking some water
  
  • non-specific
• Suyu içiyorum. = I’m drinking the water / that water
  
  • specific

This is an important Turkish pattern.

Compare:

• Kitap okuyorum. = I’m reading a book / books
• Kitabı okuyorum. = I’m reading the book

So su without -yu is completely natural here.

Biraz means a little or some.

In biraz su, it means some water / a little water.

It comes before the noun it modifies:

• biraz su = some water
• biraz ekmek = some bread
• biraz çay = a little tea

This is the normal word order.

So biraz su içiyorum is literally something like:

• I am drinking some water

Because Turkish normally prefers Subject – Object – Verb word order.

So in:

• ben biraz su içiyorum

we have:

• ben = subject
• biraz su = object
• içiyorum = verb

That gives the typical Turkish pattern: SOV.

English usually uses SVO:

• I drink water

Turkish usually uses:

• Ben su içerim.
• literally: I water drink

Turkish word order is somewhat flexible, but putting the verb at the end is the most neutral pattern.

Not exactly by itself. The comma simply links two related clauses.

In context, the relationship is understood as something like:

• My blood pressure is low, so I’m drinking some water or
• My blood pressure is low, and I’m drinking some water

Turkish often leaves this kind of connection implicit if the meaning is clear from context.

If you want to make the relationship more explicit, you could say:

• Tansiyonum düşük, bu yüzden biraz su içiyorum.
  = My blood pressure is low, so I’m drinking some water.

or:

• Tansiyonum düşük olduğu için biraz su içiyorum.
  = Because my blood pressure is low, I’m drinking some water.

So the original sentence is natural, but slightly more context-based.

Yes. In everyday Turkish, tansiyon commonly means blood pressure.

So people naturally say things like:

• Tansiyonum yüksek. = My blood pressure is high.
• Tansiyonum düşük. = My blood pressure is low.
• Tansiyon ilacı = blood pressure medicine

This is very normal spoken Turkish.

You could, but it does not mean exactly the same thing.

• Tansiyonum düşük. = My blood pressure is low.
  
  • this sounds like your current state
• Düşük tansiyonum var. = I have low blood pressure.
  
  • this sounds more like a condition or tendency

So if you mean right now my blood pressure is low, then Tansiyonum düşük is the better choice.

Yes — and that may even sound more natural in many situations.

A very common version would be:

• Tansiyonum düşük, biraz su içiyorum.

Because içiyorum already means I am drinking, the subject I is clear.

Turkish often leaves out subject pronouns unless they are needed for:

• emphasis
• contrast
• clarity

So both are correct, but the version without ben is often more natural in everyday speech.