Spelaren var nära att skjuta bollen.

Because spelaren is the definite singular form of spelare.

• en spelare = a player
• spelaren = the player

Swedish usually adds the definite article to the end of the noun instead of putting a separate word in front, so -en here works like English the.

Var is the past tense of vara, which means to be.

• är = is / are
• var = was

So this sentence is talking about a past situation, not a present one.

In this sentence, nära att + infinitive means close to doing something or almost about to do something.

So nära att skjuta means the player was close to shooting.

This is a very common Swedish pattern:

• Hon var nära att falla. = She was close to falling.
• Vi var nära att missa tåget. = We almost missed the train.

Because att is the infinitive marker, similar to English to in expressions like to shoot.

After nära in this kind of structure, Swedish normally uses:

nära att + verb infinitive

So:

• nära att skjuta = close to shooting / close to shoot

Compare:

• Spelaren var nära bollen. = The player was near the ball.
  Here there is no verb after nära, so no att is needed.

Because after att, Swedish uses the infinitive form of the verb.

• skjuta = to shoot
• sköt = shot

So:

• att skjuta = to shoot

That is why the sentence says att skjuta, not att sköt.

For the same reason as spelaren: it is the definite singular form.

• en boll = a ball
• bollen = the ball

So both the subject and the object are definite in this sentence:

• spelaren = the player
• bollen = the ball

The basic structure is:

Spelaren + var + nära att skjuta + bollen

More specifically:

• Spelaren = subject
• var = finite verb
• nära = adjective/complement
• att skjuta = infinitive phrase
• bollen = object of skjuta

A useful rule is that in a Swedish main clause, the finite verb usually comes in second position. Here the subject comes first, so var comes second.

They are similar, but not always exactly identical.

• var nära att skjuta = was close to shooting / was about to shoot
• nästan sköt = almost shot

Both suggest the action did not fully happen, but nära att often emphasizes being on the verge of doing something, while nästan simply means almost.

So in many situations they are close in meaning, but nära att can sound a bit more like the action was just about to happen.

No, not in this sentence.

Nära can mean physical closeness:

• Han stod nära målet. = He stood near the goal.

But in var nära att skjuta, it is used more figuratively, meaning close to doing something.

So Swedish uses the same word for both physical and metaphorical closeness, just like English near or close.

Yes, sometimes you can hear nära på att as well, especially in spoken or less formal language.

• Han var nära att ramla.
• Han var nära på att ramla.

Both are understandable, but nära att is the simpler and more standard form to learn first.