Jag ringer dig så fort jag kommer hem.

This is very normal in Swedish. The present tense is often used for future events when the context already makes the future meaning clear.

In Jag ringer dig så fort jag kommer hem, the time expression så fort jag kommer hem shows that the call will happen later, so Swedish does not need a special future form. English often prefers I’ll call you, but Swedish very naturally uses the present here.

Yes, that is also correct. Using ska ringa makes the idea of intention or plan a little more explicit.

So:

• Jag ringer dig ... = very natural, often the most idiomatic choice
• Jag ska ringa dig ... = also natural, with a slightly clearer sense of intention

In everyday speech, both are common.

Because dig is the object form of du.

Compare:

• du = subject form
• dig = object form

In this sentence, jag is the subject because it is the person doing the action, and dig is the object because it is the person receiving the call.

For example:

• Du ringer mig.
• Jag ringer dig.

Så fort means as soon as.

It introduces the idea that one action happens immediately after another. In this sentence, it connects the two parts:

• first: getting home
• then: calling

A close alternative is så snart, which also means as soon as. Both are common, though så fort is very frequent in everyday speech.

Because så fort jag kommer hem is a subordinate clause, and in Swedish subordinate clauses the normal word order is usually subject + verb.

So you get:

• så fort jag kommer hem

But if that whole clause comes first, then the main clause that follows has inversion:

• Så fort jag kommer hem ringer jag dig.

So:

• inside the subordinate clause: jag kommer
• in the following main clause: ringer jag

Because så fort is a conjunction that directly introduces a subordinate clause. It does not need att.

Swedish uses att in other situations, such as:

• before infinitives: Jag vill ringa
• in some clause structures

But after conjunctions like när, om, eftersom, innan, and så fort, you normally go straight into the clause:

• så fort jag kommer hem
• när jag kommer hem
• om jag hinner

Because hem by itself often works as an adverb meaning home or homeward.

Swedish commonly says:

• gå hem = go home
• komma hem = come home / get home
• åka hem = go home by transport

This is different from hemma, which means at home:

• Jag kommer hem = I get home
• Jag är hemma = I am at home

So hem expresses movement toward home, while hemma expresses location.

It can match either one in English, depending on context. In Swedish, komma hem is the normal expression for arriving at home.

So in practice, it often corresponds to:

• come home
• get home
• arrive home

English chooses between those more carefully depending on style and situation, but Swedish simply uses komma hem very naturally.

Yes. You can say:

Så fort jag kommer hem ringer jag dig.

That is completely correct and very common. When the subordinate clause comes first, the main clause follows with inversion, so jag ringer becomes ringer jag.

So both of these are correct:

• Jag ringer dig så fort jag kommer hem.
• Så fort jag kommer hem ringer jag dig.

Yes, in this kind of sentence ringa means to call someone on the phone.

So:

• Jag ringer dig = I call you / I’ll call you

The verb originally has the sense to ring, but in modern everyday Swedish it is the standard verb for making a phone call. Very often, Swedish uses ringa where English would simply say call.

In careful pronunciation, dig is traditionally pronounced something like dej in modern standard speech. In everyday spoken Swedish, that -g is usually not pronounced as a hard g.

So a learner will often hear:

• dig sounding like dej

This is very common and completely normal in spoken Swedish. The spelling stays dig, but the pronunciation is usually softer than an English speaker might expect.

Usually, yes, when Swedish is talking about the future in this kind of structure.

That is why you get:

• Jag ringer dig
• så fort jag kommer hem

Even though both actions are future from the speaker’s point of view, Swedish normally uses present tense in both clauses. This is one of the most important differences from English, which often uses will in the main clause but not in the as soon as clause.