Er du allergisk mot melk eller nøtter, kan jeg lage pasta uten saus.

Norwegian can form conditional clauses by using inverted word order (verb first), which looks like a yes/no question but functions like if.
So Er du allergisk ... , kan jeg ... means Hvis du er allergisk ... , kan jeg ... (If you are allergic..., I can...). It’s a common, natural structure.

Yes. Hvis du er ... is the straightforward if-clause version and is very common.
Er du ... is slightly more concise and can feel a bit more “spoken”/direct, but both are correct.

Because the first part is a conditional clause (Er du allergisk mot melk eller nøtter) that comes before the main clause (kan jeg lage ...). Norwegian normally separates these with a comma.

Norwegian follows the V2 rule in main clauses: the finite verb (here kan) must be in the second position.
Since the conditional clause comes first, the main clause starts with kan and the subject jeg comes right after it:

• Er du ..., kan jeg ...
  Not: Er du ..., jeg kan ...

mot literally means against/towards, and Norwegian idiomatically says allergisk mot (allergic to).
Other prepositions (like for) are not standard in this meaning.

In Norwegian, when you talk about a substance in general (like milk as an ingredient), you often use the indefinite form: melk.
Melken would typically refer to a specific milk (e.g., “the milk we bought”).

Allergies are usually expressed with the general category, and nuts is commonly treated as a plural set: nøtter.
You can say nøtt in some contexts, but nøtter is the more natural “nuts (in general)” wording.

In everyday use, eller often covers the practical meaning: milk or nuts (or both)—i.e., if either of these is a problem.
If you wanted to be extremely explicit, you could rephrase, but in this kind of allergy context the meaning is normally clear.

kan is the modal verb can / be able to / be allowed to. Here it means I can / I’m able to (I can make an alternative).
It’s a polite, practical offer.

Yes. lage pasta is common and broad: it can mean make/prepare/cook pasta depending on context.
If you want to be more specific about boiling, you might use koke pasta, but lage is very natural in offers like this.

After uten (without), Norwegian often uses the bare indefinite noun for something uncountable or “in general”: uten saus.
uten en saus would sound like without a (particular) sauce or without one sauce, which is not what you usually mean here.

Yes, you sometimes see:

• Er du allergisk ..., så kan jeg lage pasta uten saus.
  så here is like “then,” and it can make the conditional link feel extra clear. It’s optional; the original sentence is already correct.