Сегодня я купил абонемент в новый спортзал рядом с метро.

Because купил is the perfective past form, used for a completed action: the speaker bought the membership, and the action is finished.

• купил = bought / has bought
• покупал = was buying, used to buy, or sometimes bought with focus on the process rather than completion

In this sentence, the important idea is the result: today I bought it.

Абонемент usually means a pass, subscription, or membership that gives you access for a period of time.

In this context, абонемент в спортзал means something like:

• a gym membership
• a gym pass
• a subscription to use the gym

It is not usually a single ticket for one visit.

Here в is used with the accusative case because it expresses direction or destination: into / to a new gym.

So:

• в новый спортзал = to/for a new gym
• в новом спортзале would mean in the new gym and uses the prepositional case

Even though English says a membership to a gym, Russian still uses в + accusative here.

Новый agrees with спортзал.

• спортзал is masculine
• it is singular
• after в here it is in the accusative

For masculine inanimate nouns, the accusative form looks like the nominative:

• новый спортзал
  not
• нового спортзала (that would be accusative only for animate masculine nouns, or genitive in other contexts)

So новый matches спортзал correctly.

Because the expression рядом с means next to / near, and it requires the instrumental case.

So normally you get:

• рядом с домом = near the house
• рядом с парком = near the park

Here the noun is метро, which is indeclinable, so its form does not change:

• nominative: метро
• instrumental: still метро

That is why you see с метро, not a different ending.

Метро is one of the common Russian nouns that are indeclinable. That means it keeps the same form in all cases.

So you can have:

• у метро = by the metro
• в метро = in the metro
• рядом с метро = near the metro

The preposition changes, the meaning changes, but метро stays метро.

In this sentence, рядом с метро usually means near the metro station.

In everyday Russian, метро can refer to:

• the metro/subway system in general
• a metro station, depending on context

So рядом с метро is a very natural way to say near the subway/metro station.

Yes, Russian often drops subject pronouns when the meaning is clear from the verb form.

So you could also say:

• Сегодня купил абонемент в новый спортзал рядом с метро.

That still means Today I bought a membership to a new gym near the metro.

However, я is perfectly natural too. It may be used for:

• clarity
• emphasis
• a more explicit, conversational style

Yes. Russian word order is more flexible than English word order because case endings show grammatical relationships.

This sentence is neutral and natural:

• Сегодня я купил абонемент в новый спортзал рядом с метро.

But other orders are possible, for example:

• Я сегодня купил абонемент в новый спортзал рядом с метро.
• Абонемент в новый спортзал рядом с метро я купил сегодня.

These versions shift emphasis slightly:

• putting сегодня early highlights today
• putting абонемент early highlights the membership

So word order often affects focus, not basic meaning.

Usually, yes. Спортзал means gym or sports hall.

Depending on context, Russian can also use:

• тренажёрный зал = gym with exercise machines / weight room
• фитнес-клуб = fitness club
• спортзал = a general gym/sports hall

In this sentence, спортзал works well as a general word for gym.

Russian has no articles. There is no direct equivalent of English a/an or the.

So:

• абонемент can mean a membership or the membership
• новый спортзал can mean a new gym or the new gym

The exact meaning comes from context.

In this sentence, English would usually translate it as a membership to a new gym near the metro.

Because of agreement.

• абонемент is masculine singular, so in principle новый could match it too
• but word order and meaning show that новый спортзал is a phrase: new gym

So the structure is:

• купил [абонемент] [в новый спортзал] [рядом с метро]

That means:

• bought a membership
• to a new gym
• near the metro

If you wanted to say a new membership, Russian would more naturally place the adjective right next to абонемент:

• купил новый абонемент...

Yes, it is natural Russian.

A native speaker might also say things like:

• Сегодня я купил абонемент в спортзал рядом с метро.
• Сегодня купил абонемент в новый спортзал у метро.

Small differences:

• рядом с метро = near the metro
• у метро = by the metro / near the metro

Both are common. Your original sentence sounds normal and idiomatic.

The stress is:

• сегóдня
• купи́л
• абонеме́нт
• но́вый
• спортза́л
• ря́дом
• метро́

Stress matters in Russian pronunciation, so it is worth learning words together with their stress.