Compro un chilo di mele al mercato.

Italian often leaves out subject pronouns when the verb ending already makes the subject clear. Compro ends in -o, which shows it is I.

So:

• Compro = I buy / I am buying
• Io compro = also correct, but with extra emphasis, contrast, or clarity

Compro is the present indicative, first person singular, of comprare.

It can mean:

• I buy
• I am buying
• sometimes a habitual meaning, depending on context, like I buy a kilo of apples at the market

Italian present tense often covers both simple present and present progressive meanings that English separates.

Because chilo is a masculine singular noun, so it takes the masculine singular indefinite article un.

Also:

• chilo is the everyday short form of chilogrammo
• it uses un, not uno, because chilo begins with a regular k sound, not a sound that requires uno

After a quantity or measure, Italian normally uses di to link the amount to the thing being measured.

Examples:

• un chilo di mele = a kilo of apples
• due litri di latte = two liters of milk
• un pezzo di pane = a piece of bread

So here di works like English of.

Because the sentence refers to more than one apple. After a quantity expression, a countable noun is normally plural:

• un chilo di mele
• tre chili di patate
• mezzo chilo di pomodori

Using singular mela here would sound unnatural in ordinary Italian.

After expressions of quantity, Italian usually uses di + noun without an article.

So the normal pattern is:

• un chilo di mele

not usually:

• un chilo delle mele

You would use an article only if you meant a specific group of apples, for example:

• un chilo delle mele che hai comprato ieri

That means a kilo of the apples you bought yesterday.

Because Italian often uses a preposition plus a definite article with places. Mercato is masculine singular, so a + il becomes al.

So:

• a + il mercato → al mercato

This is the normal form.

Al is a contraction of a + il.

• a = to, at
• il = the
• al = to the, at the

Italian regularly combines prepositions with articles, for example:

• a + il = al
• di + il = del
• in + il = nel

It depends on context. In this sentence, with comprare, it is most naturally understood as at the market.

Italian often uses a for locations where English would use at. So al mercato can describe where the buying happens.

Yes. Italian word order is more flexible than English word order.

The sentence:

• Compro un chilo di mele al mercato

is the most neutral, straightforward order.

But you could also say:

• Al mercato compro un chilo di mele

This puts more emphasis on al mercato.

So the original version is natural and standard, but not the only possible order.