Det er venligt af dig at hjælpe mig.

Because venligt is the neuter singular / adverbial form of the adjective venlig.

In Det er venligt af dig ..., the adjective is used with det, and Danish normally uses the -t form in this kind of structure:

• en venlig person
• et venligt svar
• Det er venligt af dig

So even though dig refers to a person, the adjective agrees with det, not with dig.

Here det is a dummy subject or formal subject. English does the same thing in sentences like:

• It is kind of you to help me.

Danish often uses det er + adjective + af someone + at ... for this pattern:

• Det er venligt af dig at hjælpe mig.
• Det er sødt af hende at komme.
• Det er dumt af ham at sige det.

So det does not refer to a specific thing here. It is just the grammatical subject.

Because af is the normal preposition in this structure when you are saying that a quality belongs to a person's action:

• Det er venligt af dig ...
• Det er pænt af ham ...
• Det var dumt af mig ...

It is similar to English of you in It is kind of you ....

For dig would mean for you, which is a different idea.

Because at hjælpe is the infinitive form, like English to help.

After this pattern, Danish uses an infinitive phrase:

• Det er venligt af dig at hjælpe mig.
• Det er svært at forstå.
• Det er vigtigt at komme til tiden.

So at hjælpe mig means to help me.

Because mig is the object form of the pronoun, like English me.

Compare:

• jeg = I
• mig = me

Since hjælpe takes an object here, Danish uses mig:

• du hjælper mig
• not du hjælper jeg

Venlig can mean both kind and friendly/polite, depending on context.

In this sentence, venligt usually means something like:

• kind
• nice
• thoughtful

So the sentence sounds natural. But Danish also often uses other adjectives in similar sentences, for example:

• Det er pænt af dig at hjælpe mig.
• Det er sødt af dig at hjælpe mig.
• Det er flinkt af dig at hjælpe mig. (common in some contexts/regions)

Each one has a slightly different tone, but they are all possible.

Yes, it is natural and correct.

That said, in everyday speech many Danes might also say:

• Det er pænt af dig at hjælpe mig.
• Det var sødt af dig at hjælpe mig.
• Hvor er det venligt af dig at hjælpe mig.

So your sentence is good, but there are several other very common ways to express the same general idea.

Yes. Just change er to the tense you need:

• Det er venligt af dig at hjælpe mig.
• Det var venligt af dig at hjælpe mig.
• Det vil være venligt af dig at hjælpe mig.

In real life, var is often used if the help has already happened:

• Det var venligt af dig at hjælpe mig.

No, that is not natural Danish for this meaning.

If you want to say It is kind of you to help me, the normal pattern is:

• Det er venligt af dig at hjælpe mig.

If you say Du er venlig, that means You are kind / polite in a more general sense, not specifically that the action of helping is kind.

So Danish prefers this structure when judging an action:

• Det er + adjective + af + person + at + infinitive

The pattern is:

Det er + adjective + af + person + at + infinitive

Examples:

• Det er venligt af dig at hjælpe mig.
• Det er dumt af ham at lyve.
• Det er flot af hende at prøve.

This is a very useful pattern in Danish for commenting on someone's action.

In Danish yes/no questions, the verb usually comes before the subject:

• Er det venligt af dig at hjælpe mig?

But in real conversation, this exact question may sound slightly unusual unless you are genuinely asking whether the action counts as kind. More often, people use the statement form as a comment:

• Det er venligt af dig at hjælpe mig.

Yes, it is a bit tricky for English speakers.

A few useful points:

• v is like English v
• e is short
• g in venlig is not pronounced like a hard English g
• the ending -ligt is often reduced in connected speech

You do not need to pronounce every letter strongly. In natural speech, venligt is smoother and less fully pronounced than the spelling suggests.

The most important thing for a learner is to recognize it as the -t form of venlig and not try to pronounce the g as in go.

Yes, very easily. This pattern is productive.

For example:

• Det er venligt af dig at ringe.
• Det er sødt af dig at komme.
• Det er dumt af ham at vente så længe.
• Det er flot af hende at sige undskyld.

So once you learn the structure, you can use it with many different infinitives.