Min mand siger, at der er for meget olie i panden.

Yes, mand can mean both man and husband in Danish.

In a phrase like min mand, it normally means my husband, not my man in the general English sense. So:

• en mand = a man
• min mand = my husband

The possessive min makes it clear that this is a personal relationship.

Because mand is a common gender noun in Danish, not a neuter noun.

Danish has two grammatical genders:

• common gender: takes en, min
• neuter: takes et, mit

So:

• en mand
• min mand

If it were a neuter noun, you would use mit instead.

Siger is the present tense form of sige (to say).

In Danish, verbs do not change for different persons the way they do in English. The same form is used for I, you, he, she, we, and they.

So:

• jeg siger = I say / I am saying
• du siger = you say / you are saying
• han siger = he says / he is saying

That final -r is the normal present-tense ending for many Danish verbs.

Because at der er for meget olie i panden is a subordinate clause introduced by at (that).

So the sentence is:

• main clause: Min mand siger
• subordinate clause: at der er for meget olie i panden

Many Danish writers put a comma before a subordinate clause like this. You may also learn that Danish comma rules can vary depending on the system being used, but this comma is very common and completely normal.

Here at means that.

So:

• Min mand siger, at ... = My husband says that ...

Be careful: at can also be the infinitive marker, like English to:

• at spise = to eat

But in your sentence, at is a conjunction meaning that.

Because der er is the normal Danish way to say there is or there are.

So:

• der er olie i panden = there is oil in the pan

This der is not the same as there meaning a place. It is part of an existential structure:

• der er = there is / there are

By contrast, det er usually means it is:

• det er godt = it is good

So in this sentence, der er is the correct choice because the meaning is there is too much oil in the pan.

Because olie is treated as an uncountable noun, like oil in English.

Use:

• meget with uncountable nouns
• mange with countable plural nouns

So:

• for meget olie = too much oil
• for mange æbler = too many apples

This works very much like English much vs many.

For meget means too much.

The word for here does not mean for in the usual English sense. In this structure, it means too in the sense of more than is good, needed, or wanted.

Examples:

• for meget sukker = too much sugar
• for meget støj = too much noise
• for mange mennesker = too many people

So der er for meget olie i panden means there is more oil than there should be.

Because panden is the definite form of pande.

• en pande = a pan
• panden = the pan

Danish often uses the definite form where English also uses the, especially when talking about a specific object already understood from the situation.

So:

• olie i panden = oil in the pan

If you said i en pande, that would mean in a pan, which sounds less specific.

Yes. Pande can mean both:

• pan / frying pan
• forehead

And panden can mean either the pan or the forehead.

Context tells you which one is meant. In this sentence, because of olie i panden, the intended meaning is clearly oil in the pan, not oil on the forehead.

In this sentence, the word order is already the natural one for an existential clause:

• der er for meget olie i panden

After at, Danish subordinate clauses often have a different structure from main clauses, especially with adverbs, but here nothing looks dramatic because der er is already a fixed pattern meaning there is.

Compare:

• main clause: Der er for meget olie i panden.
• subordinate clause: ... at der er for meget olie i panden.

So even though it is a subordinate clause, the structure still looks very familiar.

Not normally.

Even though mand literally can mean man, min mand in ordinary Danish means my husband. If you translate it as my man, it will sound unnatural or give a different tone in English.

So the natural translation is:

• Min mand = my husband

Yes, because it is being used as an uncountable substance noun.

In Danish, as in English, substances like oil, water, and milk often appear without an article when speaking generally or when referring to an amount of the substance.

So:

• der er olie i panden = there is oil in the pan
• der er for meget olie i panden = there is too much oil in the pan

You would only add an article in more specific cases, for example if you were talking about a particular kind or portion of oil.