Läkaren sa att jag måste vara försiktig, så jag är tvungen att vila åtminstone i dag.

Läkaren means the doctor. The ending -en is the definite article attached to the noun.

• en läkare = a doctor
• läkaren = the doctor

Swedish usually puts the definite article at the end of the noun instead of using a separate word like the.

Both sa and sade can mean said.

• sa is very common in everyday Swedish
• sade is also correct, but can sound a little more formal or more written, depending on context

So Läkaren sa att ... is a very normal, natural way to say The doctor said that ...

Here att means that and introduces a subordinate clause:

• Läkaren sa att jag måste vara försiktig
• The doctor said that I must be careful

In English, that is often optional: The doctor said I must be careful.
In Swedish, att is very commonly included in this kind of sentence.

After att, Swedish uses subordinate clause word order. In this clause, the subject jag comes before the verb måste:

• att jag måste vara försiktig

That is the normal order here:

• att
  • subject + verb + rest

This is different from main clause word order, where Swedish often puts the finite verb in second position.

Because försiktig describes jag, and jag refers to a person. The adjective agrees with the common form used for a person here.

• Jag måste vara försiktig = I must be careful

You would use försiktigt when the adjective is functioning differently, often more like an adverb:

• Kör försiktigt = Drive carefully

So here:

• vara försiktig = be careful
• not vara försiktigt

Both express necessity, but they are not always identical in feel.

• måste = must / have to
• är tvungen att = am forced to / have to / am obliged to

In many situations, they are close in meaning. But är tvungen att can feel a bit stronger or more like the situation leaves no choice.

In this sentence:

• jag måste vara försiktig = the doctor says this is necessary
• jag är tvungen att vila = as a result, I have no real choice but to rest

Using both in the same sentence sounds natural and avoids repeating the exact same structure.

Because the expression is vara tvungen att + infinitive.

• Jag är tvungen att vila
• I have to rest

This is a fixed pattern in Swedish:

• är tvungen att gå = have to go
• är tvungen att vänta = have to wait

So the att here is the infinitive marker, similar to to in English.

Because after att in är tvungen att vila, the verb is in the infinitive form.

• vila = to rest
• vilar = rest / is resting in present tense

Compare:

• Jag vilar = I am resting / I rest
• Jag är tvungen att vila = I have to rest

So vila is correct because it follows att.

Here så means so in the sense of therefore / as a result.

• Läkaren sa att jag måste vara försiktig, så jag är tvungen att vila ...
• The doctor said that I must be careful, so I have to rest ...

It links the first idea to the consequence in the second clause.

Because så here is being used as a coordinating conjunction, and the clause after it keeps normal main clause word order:

• så jag är tvungen att vila

If another element had been placed first in the clause, then the verb would come second. For example:

• I dag är jag tvungen att vila

But here the subject jag comes first, so the normal order is:

• jag är

Åtminstone means at least.

In this sentence:

• vila åtminstone i dag = rest at least today

Its placement is flexible, though different positions may shift the emphasis a little:

• Jag är tvungen att vila åtminstone i dag = I have to rest at least today
• Jag är åtminstone tvungen att vila i dag = at least, I have to rest today
• Åtminstone i dag är jag tvungen att vila = at least today, I have to rest

The version in your sentence is very natural.

Because i dag is the normal expression for today.

• i dag = today
• literally, historically, it is like in day, but you should learn it as a fixed time expression

Modern Swedish also often writes it as one word:

• idag

Both i dag and idag are common. Many learners will see both.

Yes. Försiktig can mean careful, cautious, or being careful, depending on context.

Examples:

• Var försiktig! = Be careful!
• Hon är försiktig = She is careful / cautious

In your sentence, be careful is probably the most natural English equivalent, especially in a health-related situation.

It is very common and natural to put a comma there because two clauses are being linked:

• Läkaren sa att jag måste vara försiktig, så jag är tvungen att vila ...

In less formal writing, Swedish punctuation can sometimes be lighter than English, but this comma is perfectly normal and helpful for readability.

Yes, absolutely.

• Jag måste vila = I must rest / I have to rest
• Jag är tvungen att vila = I have to rest / I am forced to rest

Both are correct. Jag måste vila is shorter and very common.
Jag är tvungen att vila can sound a bit more emphatic, as if the circumstances make it unavoidable.

So the original sentence could also have been:

• Läkaren sa att jag måste vara försiktig, så jag måste vila åtminstone i dag.

That would still be correct, but slightly more repetitive.