Learn Hardcore Swedish: Hon svarar snabbt på mejlet och förklarar lugnt vad jag ska göra. - She answers the email quickly and calmly explains what I should do.

The sentence talks about a specific email (probably already known in the context), so Swedish uses the definite suffix -et instead of a separate word like the.

What’s the difference between hon and henne? Why is it Hon svarar…?

Hon = she (subject form)
Henne = her (object form)

Use hon when it’s the subject, i.e. the one doing the action:

Hon svarar snabbt. – She answers quickly.

Use henne when it’s the object, i.e. the one receiving the action:

Jag ringer henne. – I call her.

In the sentence, hon is the one who answers and explains, so the subject form is required.

Why are snabbt and lugnt with a -t at the end? Why not snabb and lugn?

Snabb and lugn are adjectives:

en snabb bil – a fast car
en lugn person – a calm person

To make many adverbs in Swedish (how something is done), you add -t to the adjective:

snabbt – quickly
lugnt – calmly

So:

Hon svarar snabbt. – She answers quickly.
Hon förklarar lugnt. – She explains calmly.

Is the word order with the adverbs fixed? Can I say Hon snabbt svarar på mejlet?

The normal word order is:
subject – verb – (object) – adverb

So:

Hon svarar snabbt på mejlet.
Hon förklarar lugnt vad jag ska göra.

You can’t just move the adverb in front of the verb in a neutral statement like in English poetic style; Hon snabbt svarar… sounds wrong in modern Swedish.

Adverbs like snabbt, lugnt usually come after the main verb in simple main clauses.

Why is it förklarar lugnt and not förklarar lugn?

Same reason as with snabbt:

lugn is an adjective = calm (describing a noun)
lugnt is an adverb = calmly (describing how she explains)

Examples:

Hon är lugn. – She is calm. (describing her)
Hon förklarar lugnt. – She explains calmly. (describing how she explains)

Why does the second verb come as och förklarar, without repeating hon?

In Swedish, if two verbs share the same subject, you normally mention the subject only once and link the verbs with och:

Hon svarar snabbt på mejlet och förklarar lugnt…

You could say Hon svarar… och hon förklarar…, but it sounds heavier and is usually only used for emphasis or special style. The shorter version is the normal one.

In vad jag ska göra, why is the verb after the subject? In questions I thought the verb comes early, like Vad ska jag göra?

Two different things:

Main question (direct question):
- Vad ska jag göra? – What should I do?
  Here the verb (ska) comes right after vad.
Embedded / indirect question (inside a larger sentence):
- Hon förklarar vad jag ska göra. – She explains what I should do.
  Here vad jag ska göra is a subordinate clause, so the order is:
  question word – subject – verb – rest

So:

Direct: Vad ska jag göra?
Indirect: Hon förklarar vad jag ska göra.

What exactly does ska mean in vad jag ska göra? Is it “will do”, “should do”, or “must do”?

Ska is flexible and depends on context. Common meanings:

Planned / expected future:
- Jag ska jobba imorgon. – I’m going to work tomorrow.
Obligation / instruction (mild “should/are supposed to”):
- Det här är vad du ska göra. – This is what you should / are supposed to do.

In vad jag ska göra here, it’s about instructions: what I’m supposed to do / what I should do next. It’s not as strong as “must”, and not just a neutral “will” either.

Why is the tense just svarar and förklarar? Could this also refer to future actions?

The Swedish present tense can cover:

actions happening now
habitual actions
sometimes near future (especially with a time expression)

Here, without extra context, it most naturally means something like:

She (normally / regularly) replies quickly to the email and calmly explains what I should do.
or
Right now, she replies quickly and calmly explains…

If you want to clearly emphasize future, you’d typically add time:

Imorgon svarar hon på mejlet och förklarar vad jag ska göra. – Tomorrow she’ll answer the email and explain what I should do.