Det kunne være hyggeligt. Det kan jeg godt. Hold mig opdateret.

In both cases, det refers to something already understood from context.

• In Det kunne være hyggeligt, det usually means that idea / that plan / doing that.
• In Det kan jeg godt, det means that in the sense of that thing you mentioned.

English sometimes uses that, it, or even leaves this kind of reference more vague. Danish very often uses det explicitly.

Kunne is the past form of kan, but after modal verbs Danish often uses the past form to sound more tentative, polite, or less definite.

So Det kunne være hyggeligt does not usually talk about the past. It means something like:

• That could be nice
• That might be nice
• That would be nice

Compared with Det kan være hyggeligt, kunne sounds softer and more hypothetical.

Because the adjective agrees with det, which is grammatically neuter.

• common gender: en hyggelig aften
• neuter: et hyggeligt sted
• after det: Det er hyggeligt

So in Det kunne være hyggeligt, the -t is there because the thing being referred to by det is treated as neuter.

Not exactly. Hyggeligt is one of those very Danish words with a wider emotional feel.

It can suggest something like:

• cozy
• pleasant
• warm
• friendly
• comfortable
• enjoyable in a relaxed, social way

So Det kunne være hyggeligt often implies more than just nice. It suggests that the situation would feel warm, pleasant, and enjoyable.

This is because Danish follows the verb-second rule in main clauses.

If det is placed first for emphasis or as the topic, the finite verb must come second:

• Det kan jeg godt
• I dag kommer han
• Så tager vi afsted

So once det is in first position, kan must come next, and jeg comes after that.

Jeg kan det godt is a different sentence pattern and would not sound the same in meaning or emphasis.

Here godt does not mean simply well in the usual English sense. It works more like a small modal particle or adverb that makes the sentence sound more natural, reassuring, or willing.

Det kan jeg godt often means:

• Yes, I can do that
• That’s fine
• Sure, I can
• I don’t mind

Without godt, Det kan jeg is possible, but it can sound more bare or more strongly focused on ability alone.

It can express any of those, depending on context.

Common possibilities are:

• ability: I can do that
• willingness: I’m happy to do that
• agreement/acceptance: That works for me

That is why this phrase is so common in Danish conversation. It is flexible and often sounds very natural as a positive response.

Because it is an imperative sentence, meaning a command or request.

In Danish imperatives, the subject is usually left out, just like in English:

• Hold mig opdateret = Keep me updated
• Kom her = Come here
• Vent lidt = Wait a moment

The understood subject is you.

Here opdateret is used like an adjective meaning updated.

The pattern is:

holde + person + adjective/past participle

So:

• Hold mig opdateret
• Hold mig informeret
• Hold døren lukket

This is very similar to English keep me updated.
So holde here does not mean physically hold. It is part of an idiomatic structure meaning keep someone in a certain state.

Yes, all three are natural everyday Danish.

Some common variations are:

• Det kunne være rigtig hyggeligt
  adds emphasis: really nice / really cozy
• Det kan jeg sagtens
  sounds like I can easily do that
• Hold mig lige opdateret
  lige often softens the request a little
• Hold mig gerne opdateret
  a polite way to say do keep me updated

So the original versions are perfectly natural, but Danish often uses small words like lige, godt, and gerne to adjust tone.