Jeg vil spise hvad som helst, for jeg er meget sulten.

Here vil most naturally means want to or am willing to.

So Jeg vil spise hvad som helst is not mainly about the future. It expresses willingness/desire: I’ll eat anything / I’m willing to eat anything.

Danish ville can sometimes overlap with English will, but in a sentence about hunger, the sense is clearly wanting rather than simple future.

Because vil is a modal verb, and it combines with an infinitive:

• jeg spiser = I am eating / I eat
• jeg vil spise = I want to eat / I will eat

So vil spise gives the idea of intention or willingness, not just the action itself.

After modal verbs in Danish, the infinitive usually comes without at.

Common modal verbs include:

• vil = want to / will
• kan = can
• skal = shall / must / am supposed to
• må = may / must
• bør = ought to

So:

• Jeg vil spise
• not Jeg vil at spise

This is similar to English, where we say I can eat, not I can to eat.

Hvad som helst is a fixed expression meaning anything, whatever at all, or absolutely anything.

Literally, it is built from:

• hvad = what
• som helst = something like soever / at all / you like

So the full phrase has a strong free choice meaning: no preference, no restriction.

Examples:

• Jeg spiser hvad som helst. = I eat anything.
• Du kan vælge hvad som helst. = You can choose anything.

Yes. This is a very useful pattern in Danish.

Some common examples:

• hvem som helst = anyone
• hvad som helst = anything
• hvor som helst = anywhere
• hvornår som helst = anytime
• hvilken som helst = any / whichever

So som helst helps turn question words into free-choice expressions.

Not with exactly the same meaning.

• noget usually means something
• hvad som helst means anything

Compare:

• Jeg vil spise noget. = I want to eat something.
• Jeg vil spise hvad som helst. = I’ll eat anything.

The second sentence is much stronger: it means the speaker is not picky at all.

Yes. In this sentence, for means because.

That may look strange at first, since learners often first meet for meaning for, but Danish for also works as a conjunction meaning because/since:

• Jeg vil spise hvad som helst, for jeg er meget sulten.

So here it introduces the reason for the first clause.

Both can often be translated as because, but they are not used in exactly the same way.

In this sentence, for links two main clauses:

• Jeg vil spise hvad som helst
• jeg er meget sulten

That makes the sentence sound like: statement + explanation.

Fordi introduces a subordinate clause:

• Jeg vil spise hvad som helst, fordi jeg er meget sulten.

That version is also correct and natural.

A useful difference shows up when there is a negation or adverb:

• ..., for jeg er ikke sulten
• ..., fordi jeg ikke er sulten

So for keeps main-clause word order, while fordi normally gives subordinate-clause word order.

Because jeg refers to one person, so the adjective is singular.

Here sulten is a predicate adjective after er:

• jeg er sulten = singular
• vi er sultne = plural

So:

• Jeg er meget sulten = correct
• Vi er meget sultne = plural version

Because the sentence contains two clauses, and for connects them:

• Jeg vil spise hvad som helst
• for jeg er meget sulten

In standard Danish punctuation, a comma is normally used here to separate the clauses.

Yes, it is natural and correct.

It sounds perfectly fine as it is:

• Jeg vil spise hvad som helst, for jeg er meget sulten.

A very common alternative would be:

• Jeg er så sulten, at jeg kan spise hvad som helst.

That means:

• I’m so hungry that I could eat anything.

So your original sentence is good, but there are other idiomatic ways to express the same idea.