Chiedo al barista un bicchiere d’acqua fresca.

Because Italian usually drops subject pronouns when the verb ending already shows who is doing the action.

Chiedo ends in -o, which tells you it is I. So Chiedo by itself already means I ask or I am asking.

You can add io for emphasis or contrast:

Io chiedo al barista un bicchiere d’acqua fresca, non tu.

But in a normal sentence, leaving io out is more natural.

Chiedo is the present indicative of chiedere.

Depending on context, it can mean:

• I ask
• I am asking
• I do ask

Italian often uses the simple present where English might use either the simple present or the present progressive.

Here chiedere means to ask for or to request.

That is important because English often says:

I ask the bartender for a glass of water

But Italian structures it differently:

chiedere qualcosa a qualcuno
literally, to ask something to someone

So in this sentence:

• un bicchiere d’acqua fresca = the thing requested
• al barista = the person you ask

Al is the contraction of a + il.

So:

• a = to
• il barista = the bartender / the barman / the person working at the bar
• al barista = to the bartender

With chiedere, the person you ask is introduced by a.

Also, the contraction is standard and expected:

• a + il = al
• a + la = alla
• a + i = ai
• and so on

Because Italian does not copy the English pattern ask someone for something.

In Italian, the normal pattern is:

chiedere qualcosa a qualcuno

So you do not usually say chiedere per here.

That means:

• English: I ask the bartender for a glass of water
• Italian: Chiedo al barista un bicchiere d’acqua

For an English speaker, this is one of the most common structure differences to remember.

Because it is the direct object: the thing being requested.

In this sentence:

• al barista = indirect object, marked by a
• un bicchiere d’acqua fresca = direct object, with no preposition

So the sentence breaks down like this:

• Chiedo = I ask
• al barista = to the bartender
• un bicchiere d’acqua fresca = a glass of cool water

Because di often becomes d’ before a vowel.

So:

• di acqua becomes d’acqua

This is very common in expressions like:

• un bicchiere d’acqua = a glass of water
• una bottiglia d’acqua = a bottle of water

It is the same di, just contracted for smoother pronunciation.

Because fresca describes acqua, not bicchiere.

In: un bicchiere d’acqua fresca

the adjective agrees with acqua, which is:

• feminine
• singular

So:

• acqua fresca = cool/fresh water

If the adjective described bicchiere, it would be masculine:

• un bicchiere fresco

But that would mean the glass is cool, not the water.

In this sentence:

• barista is masculine because you have il inside al
  al barista = a + il barista
• bicchiere is masculine, so you use un bicchiere
• acqua is feminine, so the adjective is fresca

A useful detail: barista can be masculine or feminine in Italian depending on the article:

• il barista = male barista / bartender
• la barista = female barista / bartender

Yes. Italian word order is more flexible than English.

You can also say:

Chiedo un bicchiere d’acqua fresca al barista.

Both are grammatical.

The difference is mostly about emphasis or style:

• Chiedo al barista un bicchiere d’acqua fresca puts the person asked earlier
• Chiedo un bicchiere d’acqua fresca al barista puts the requested item earlier

In many everyday contexts, the second order may sound a bit more neutral.

Not exactly.

• fresca usually means cool or pleasantly cool
• fredda means cold

So acqua fresca is often more like cool water than ice-cold water.

In many real situations, acqua fresca sounds natural if you want water that is not warm. If you specifically want very cold water, acqua fredda would be stronger.

It is grammatically correct and understandable, but it sounds a bit like a textbook or narrative sentence.

In a real bar, people often use more direct and polite request formulas, such as:

• Un bicchiere d’acqua, per favore.
• Mi dà un bicchiere d’acqua, per favore?
• Posso avere un bicchiere d’acqua fresca?

So Chiedo al barista un bicchiere d’acqua fresca is perfectly good for learning grammar, but it is not the most typical way to place the order yourself.