Штрафной балл уже записан.

In Russian, the verb to be is normally not expressed in the present tense.

So:

• Штрафной балл уже записан = The penalty point is already recorded / has already been entered

Russian does use forms of быть in the past and future:

• Штрафной балл был записан = The penalty point was recorded
• Штрафной балл будет записан = The penalty point will be recorded

So the present-tense is is simply understood.

Уже means already.

In this sentence, it shows that the action has been completed before now:

• Штрафной балл уже записан = The penalty point has already been entered

It often adds the idea of this has been done now; it’s not pending anymore.

Записан is the short form of the passive participle, and it is used as part of the predicate:

• Штрафной балл уже записан = The penalty point is already recorded

Записанный is the full form, usually used like an adjective before a noun:

• записанный балл = the recorded point

A useful rule of thumb:

• short form = usually after the noun, as the main statement
• full form = usually before the noun, describing it

So here, because the sentence is saying what state the penalty point is in, записан is the natural form.

Because it agrees with балл, which is:

• masculine
• singular
• nominative

Short-form passive participles change for gender and number:

• masculine: записан
• feminine: записана
• neuter: записано
• plural: записаны

For example:

• Ошибка уже записана = The mistake is already recorded
• Имена уже записаны = The names are already written down

Штрафной is an adjective modifying балл, so it has to agree with it.

Since балл is masculine singular nominative, the adjective is also masculine singular nominative:

• штрафной балл

If the noun changed, the adjective would change too:

• штрафная минута = penalty minute
• штрафное очко = penalty point in a neuter-noun context
• штрафные баллы = penalty points

It is in the nominative case because it is the grammatical subject of the sentence.

The sentence is basically:

• Penalty point — already recorded

So штрафной балл is the thing being talked about, which is why it appears in the nominative.

It can mean any of those, depending on context.

The verb записать has a broad meaning: to write down, to record, to enter, to make a note of.

So:

• in a notebook context: written down
• in a system or register: entered
• in an official record: recorded

In Штрафной балл уже записан, the most natural English translation is often:

• The penalty point has already been recorded
• or ...has already been entered

Russian often expresses this idea with a short passive participle and no present-tense to be.

So where English says:

• has been recorded
• is already entered

Russian can simply say:

• уже записан

This often gives a result-state meaning: the action is complete, and the result now exists.

So Штрафной балл уже записан focuses on the current state: the penalty point is now on the record.

Yes. Russian word order is fairly flexible, and changing it often changes emphasis, not the basic meaning.

For example:

• Штрафной балл уже записан
  neutral; the penalty point is already recorded

• Уже записан штрафной балл
  stronger focus on already recorded

• Записан уже штрафной балл
  possible, but more marked and context-dependent

The version you gave is a normal, neutral way to say it.

Russian has no articles.

So штрафной балл can mean:

• a penalty point
• the penalty point

Which one is meant depends on context.

That is normal in Russian, and learners have to get used to understanding definiteness from the situation rather than from a word like the.

Yes, but it means something slightly different in structure.

• Штрафной балл уже записан = The penalty point is already recorded / has already been entered
  This is passive/resultative and focuses on the state.

• Штрафной балл уже записали = They already recorded the penalty point
  This is an active verb in the plural, often with an indefinite they meaning someone did it.

Both can work, but записан sounds more like the point is now officially on record, while записали points more to the action done by people.

It comes from the verb записать, which is usually perfective.

• записать = to write down / record / enter
• записан = recorded / entered

Because it comes from a perfective verb, it naturally suggests a completed action and its result.

That is why уже записан feels very natural: it means the recording has already been completed.