Questa rivista è interessante, ne compro una seconda.

Here ne means of it / of them, referring back to rivista.

So:

• Questa rivista è interessante = This magazine is interesting.
• Ne compro una seconda = I’m buying a second one / I’ll buy another copy of it.

In Italian, ne is often used when you are talking about a quantity taken from something already mentioned.

For example:

• Compro due riviste = I buy two magazines.
• Ne compro due = I buy two of them.

In your sentence, una seconda works the same way: a second one.

Because ne is a clitic pronoun, and in normal finite verb forms it usually goes before the verb.

So Italian says:

• ne compro
• ne voglio
• ne ho

not:

• compro ne

This is a very common pronoun position rule in Italian.
With infinitives, gerunds, and affirmative commands, pronouns can attach to the end instead, but here compro is a normal present-tense verb, so ne goes before it.

Because Italian often leaves out a noun when it is already clear from context.

So:

• ne compro una seconda

really means:

• ne compro una seconda rivista

But repeating rivista would sound unnecessary here.
Just like in English, you can say a second one instead of a second magazine.

It means a second one or another copy.

Literally, seconda is second, feminine singular, agreeing with the omitted noun rivista.

So the structure is:

• una = one / a
• seconda = second

Together: a second one.

In this context, it suggests buying an additional copy of the magazine that was just mentioned.

Because una seconda means a second one, while la seconda would mean the second one.

That is an important difference:

• una seconda = another one, a second one
• la seconda = the second one

In your sentence, the speaker is not identifying a specific second magazine in a series. They are saying they want to buy an additional copy, so una seconda is the right choice.

Yes, in many situations you could say ne compro un’altra, meaning I’m buying another one.

But there is a slight nuance:

• una seconda emphasizes that it is a second copy
• un’altra simply means another one

So:

• ne compro una seconda = I buy a second one
• ne compro un’altra = I buy another one

Both can work, but una seconda is a bit more explicit about number.

Because rivista is a feminine singular noun, and demonstratives must agree with the noun.

So:

• questo = this, masculine singular
• questa = this, feminine singular

Examples:

• questo libro = this book
• questa rivista = this magazine

The same agreement rule applies to other words connected to the noun.

Because it agrees with the omitted noun rivista, which is feminine singular.

Even when the noun is not repeated, Italian still keeps agreement:

• una seconda rivista = a second magazine
• ne compro una seconda = I buy a second one

The word seconda stays feminine because the hidden noun is still rivista.

Because interessante is one of many Italian adjectives that have the same form for masculine and feminine in the singular.

So you get:

• un libro interessante
• una rivista interessante

The adjective changes only in the plural:

• libri interessanti
• riviste interessanti

So the feminine singular does not require a different form here.

Because Italian often omits subject pronouns when they are not needed.

The verb form compro already tells you the subject is I.

• compro = I buy
• compriamo = we buy
• comprano = they buy

So io compro is possible, but usually io is only added for emphasis, contrast, or clarity.

In this sentence, compro by itself is perfectly natural.

Because è is the verb is, from essere, and it must be written with a grave accent.

This distinguishes it from e, which means and.

So:

• è = is
• e = and

This is a very important spelling difference in Italian.

Yes, that can happen.

Italian present tense often covers meanings that English expresses with:

• I buy
• I’m buying
• I’ll buy

In this sentence, ne compro una seconda can sound like a present decision: I’m buying a second one or I’ll buy another copy.

Italian uses the present tense very naturally for immediate intentions and near-future actions.

The comma is understandable and quite common in informal writing, because the second clause follows naturally from the first.

However, in more careful writing, many people would prefer:

• Questa rivista è interessante; ne compro una seconda.
• Questa rivista è interessante, quindi ne compro una seconda.
• Questa rivista è interessante. Ne compro una seconda.

So the original punctuation is not strange, but there are other versions that may look more formal or clearer.