Когда я долго сижу за компьютером, у меня болит затылок.

Когда means when.

In this sentence, Когда я долго сижу за компьютером is a subordinate clause: When I sit at the computer for a long time. Russian normally separates this kind of clause from the main clause with a comma.

So the structure is:

• Когда я долго сижу за компьютером, = When I sit at the computer for a long time
• у меня болит затылок = the back of my head hurts

The comma is required here.

In Russian, the present tense is often used for habitual or repeated situations, just like in English:

• Когда я долго сижу за компьютером...
  When I sit at the computer for a long time...

It does not have to mean only right now. It can mean whenever this happens or in cases like this.

Долго means for a long time.

So:

• я долго сижу = I sit for a long time
• Когда я долго сижу за компьютером = When I sit at the computer for a long time

It is an adverb, so it describes the action сижу.

Because the verb is сидеть (to sit), and its я-form is irregular-looking for many learners:

• я сижу = I sit
• ты сидишь
• он / она сидит
• мы сидим
• вы сидите
• они сидят

So сижу is simply the correct 1st person singular present form of сидеть.

Because за can take different cases depending on the meaning.

Here, за компьютером means at the computer or literally behind the computer, describing a location. With this meaning, Russian uses the instrumental case:

• компьютер → компьютером

Compare:

• сидеть за компьютером = to sit at the computer
• сесть за компьютер = to sit down at the computer

The second one involves movement toward a position, so it uses a different case.

Russian very often expresses pain with the pattern:

• у + person in the genitive + болит / болят + body part

So:

• у меня болит затылок = literally at me, the back of the head hurts
• natural English: the back of my head hurts

This is one of the most common Russian patterns for physical pain:

• У меня болит голова. = My head hurts.
• У меня болит спина. = My back hurts.
• У меня болят глаза. = My eyes hurt.

You can say мой затылок болит, but it sounds less natural in ordinary speech. У меня болит... is the standard everyday way.

Because the expression у меня requires the genitive.

The preposition у often means something like by, at, or in the possession of, and it is followed by the genitive:

• я → меня
• ты → тебя
• он → него
• она → неё

So:

• у меня = with me / for me / I have / my

  In pain expressions, у меня is just the normal structure:

• У меня болит рука.
• У меня болит шея.

Because затылок is the grammatical subject of болит.

In the structure у меня болит затылок:

• у меня = marks the person affected
• болит = hurts
• затылок = the thing that hurts

So затылок stays in the nominative singular.

This is why Russian says:

• болит затылок = the back of the head hurts

If there were several things hurting, Russian would use болят:

• У меня болят глаза. = My eyes hurt.

Затылок means the back of the head, especially the part behind and above the neck.

It is more specific than голова (head). So:

• У меня болит голова = I have a headache / My head hurts.
• У меня болит затылок = The back of my head hurts.

This often suggests pain in a particular area rather than the whole head.

Because болит comes from болеть in the sense to hurt / to ache.

In this sentence:

• болит затылок = the back of my head hurts

Compare two meanings of болеть:

1. болеть = to hurt / ache
   
   • У меня болит спина.
2. болеть = to be ill / be sick
   
   • Он болеет. = He is ill.

So болит here is exactly the right form for physical pain in a body part.

Both are possible, but they emphasize things differently.

The neutral, most common order is:

• У меня болит затылок.

This presents the situation naturally: As for me, the back of my head hurts.

You could also say:

• Затылок у меня болит.

That puts more emphasis on затылок, maybe in contrast with something else:

• Не шея, а затылок у меня болит.
  Not my neck, but the back of my head hurts.

So the original sentence uses the most neutral everyday order.

Sometimes yes, but not always.

Literally, сидеть за компьютером means to sit at the computer. In context, it can imply:

• working on the computer
• studying on the computer
• spending time on the computer
• using the computer in general

So in English, the best translation depends on context. But the Russian itself specifically says sit at the computer, not necessarily work.

Yes, absolutely. That is a very natural interpretation.

Russian present tense plus когда often gives this kind of general repeated meaning:

• Когда я долго сижу за компьютером, у меня болит затылок.
• Whenever I sit at the computer for too long, the back of my head hurts.

That is probably one of the best natural English renderings.

Then болит would usually become болят, because the subject would be plural.

For example:

• У меня болят глаза. = My eyes hurt.
• Когда я долго сижу за компьютером, у меня болят глаза.

So:

• болит = singular thing hurts
• болят = plural things hurt

In the original sentence, затылок is singular, so болит is correct.