Har du et forslag til, hvad vi skal spise i aften?

Because this is a direct question. In Danish, yes/no questions usually put the finite verb before the subject.

• Statement: Du har et forslag.
• Question: Har du et forslag?

That is similar to English You have... → Have you...?

Because forslag is a neuter noun in Danish, so its indefinite article is et.

• et forslag = a suggestion
• forslaget = the suggestion

Danish nouns are either common gender or neuter, and you usually just have to learn the gender with the noun.

Here, til goes with forslag and means something like for or as to.

So et forslag til, hvad vi skal spise means a suggestion for what we should eat.

This is a very common Danish pattern:

• et forslag til en løsning = a suggestion for a solution
• et forslag til, hvad vi kan gøre = a suggestion for what we can do

Because hvad vi skal spise i aften is a subordinate clause, and Danish often marks that with a comma.

In this sentence, the comma separates:

• main part: Har du et forslag til
• subordinate clause: hvad vi skal spise i aften

You may also see the sentence written without that comma, depending on the comma style being used in Danish. So the comma is about punctuation, not meaning.

Because this is an embedded question, not a standalone question.

A direct question is:

• Hvad skal vi spise i aften?

But after til it becomes part of a bigger sentence, so Danish uses subordinate-clause word order:

• ... hvad vi skal spise i aften

This is similar to English:

• direct: What should we eat tonight?
• embedded: Do you know what we should eat tonight?

Here skal does not have to mean strong obligation. In this kind of sentence, it often means something like:

• should
• are going to
• are supposed to

So hvad vi skal spise i aften can be understood as what we should eat tonight or what we’re going to eat tonight, depending on context.

Because after a modal verb such as skal, Danish normally uses the bare infinitive, without at.

So:

• vi skal spise
• vi kan spise
• vi vil spise

not:

• vi skal at spise

This works like English we should eat, not we should to eat.

Because hvad means what in a general, open-ended way.

Here the speaker is asking for an idea in general: what should we eat?

You would use hvilken / hvilket / hvilke more for which, especially when choosing among more specific options:

• Hvilken pizza skal vi bestille? = Which pizza should we order?
• Hvilket sted skal vi spise på? = Which place should we eat at?

So hvad is the natural choice in this sentence.

I aften is the normal Danish expression for tonight / this evening.

It is a fixed time expression, just like:

• i dag = today
• i morgen = tomorrow
• i aften = tonight

A useful contrast is:

• i aften = tonight, this specific evening
• om aftenen = in the evening, evenings in general

So here i aften is correct because the question is about tonight.

Yes, Danish word order allows some movement of time expressions, but the version in your sentence is the most neutral and natural:

• Har du et forslag til, hvad vi skal spise i aften?

You could also hear or see variants like:

• ... hvad vi i aften skal spise

That is still grammatical, but it sounds a bit more marked or formal. For everyday Danish, the original order is the safest choice.