Min mor siger også velbekomme, når jeg takker hende for aftensmaden.

Because mor is a common-gender noun in Danish. With common-gender singular nouns, you use min.

A quick comparison:

• min = common gender singular
• mit = neuter singular
• mine = plural

So:

• min mor = my mother
• mit hus = my house
• mine bøger = my books

That is the normal word order in a Danish main clause.

Danish usually follows the V2 rule, which means the finite verb comes in the second position. Here:

• Min mor = first element
• siger = finite verb in second position
• også = adverb after the verb

So Min mor siger også velbekomme is the neutral, natural order.

Because velbekomme is the actual expression being said, not a full subordinate clause.

Danish often uses sige directly with the word or phrase someone says:

• Hun siger hej
• Han sagde tak
• Min mor siger velbekomme

You use at when what follows is a full clause:

• Hun siger, at hun er træt = She says that she is tired

So in this sentence, velbekomme is just the expression your mother says, so no at is needed.

Here velbekomme is a polite set phrase said after someone thanks you for food. In this context, it is basically like you’re welcome.

It is especially common:

• when someone thanks you for a meal
• when serving food, where it can feel closer to enjoy your meal

So in this sentence, the meaning is specifically tied to the meal situation.

Because når is used for something that happens regularly, generally, or whenever the situation occurs.

Here the sentence describes a habit:

• when/whenever I thank her for dinner, my mother also says velbekomme

Compare:

• når = when / whenever, in general or repeated situations
• da = when, for a single event in the past
• hvis = if

So når is the right choice because this is not one specific past event and not a conditional if situation.

Because Danish often uses the present tense for habitual or general actions, just like English does.

So når jeg takker hende means:

• when I thank her
• or more naturally in context, whenever I thank her

It does not have to mean only right now. It can describe something that regularly happens.

Because hende is the object form of the pronoun, while hun is the subject form.

In this sentence:

• jeg is the subject
• takker is the verb
• hende is the person receiving the action, so it must be the object form

Compare:

• Hun siger velbekomme = She says you’re welcome
• Jeg takker hende = I thank her

Because the Danish verb takke normally follows the pattern:

takke nogen for noget
= thank someone for something

So:

• jeg takker hende for aftensmaden
• literally: I thank her for the dinner

This is just the standard construction of the verb. You normally cannot leave out for here.

Because aftensmaden is the definite form: the dinner / the evening meal.

• aftensmad = dinner, evening meal
• aftensmaden = the dinner, the evening meal

In Danish, it is very common to use the definite form when referring to a specific meal already understood from the situation. English often uses just dinner where Danish prefers aftensmaden.

Because Danish forms compound nouns as a single word.

Here:

• aften = evening
• mad = food

Together they make:

• aftensmad = evening meal / dinner

Then the definite ending -en is added:

• aftensmaden = the dinner

This is very typical in Danish. Where English often writes two words, Danish often writes one compound word.

Yes. You can say:

Når jeg takker hende for aftensmaden, siger min mor også velbekomme.

That is completely correct.

But notice what happens in the main clause afterward:

• siger comes before min mor

This is because Danish still keeps the finite verb in second position. When the sentence starts with the når clause, that whole clause takes the first position, so the main verb comes next.

Because in standard Danish writing, a subordinate clause is usually separated by a comma.

Here når jeg takker hende for aftensmaden is a subordinate clause introduced by når, so the comma before it is normal Danish punctuation.

This is one place where Danish punctuation can look a bit more explicit than English punctuation.