Hun er syk i dag, og skulderen gjør vondt, så hun venter på venterommet.

Norwegian uses the set expression å gjøre vondt to mean “to hurt/ache.” Literally “to do hurt,” it’s the natural way to say something causes pain:

• Det gjør vondt. = It hurts.
• Skulderen gjør vondt. = The shoulder hurts.

Using er vondt would describe a permanent quality (“is painful”) rather than an experience of pain, and føles vondt is possible but usually sounds more evaluative (“feels bad/painful”), not the default for aches.

Note the form vondt is the neuter of the adjective vond used adverbially in this construction.

Yes, and many would find that even more idiomatic for body-part pain. Two very natural options are:

• Hun har vondt i skulderen.
• Det gjør vondt i skulderen.

Your sentence’s Skulderen gjør vondt is understandable and acceptable, but “har vondt i …” is extremely common in everyday speech.

With body parts, Norwegian often uses the definite form without a possessive when the owner is clear from context:

• Hun har vondt i skulderen. (not necessarily “her shoulder” stated, but understood)

If you add a possessive, prefer the reflexive when the possessor is the subject:

• Hun holdt skulderen sin. = She held her (own) shoulder.

Use hennes when the possessor is someone else or when you want to emphasize non-reflexive possession:

• Hun så at mannen skadet skulderen hennes. = She saw that the man injured her shoulder (someone else’s perspective).

Norwegian typically puts a comma between coordinated main clauses:

• Hun er syk i dag, og skulderen gjør vondt, så hun venter på venterommet.

Both og and så connect independent clauses here, so commas are expected by the standard comma rules. (Writers sometimes omit the first comma in informal texts, but it’s recommended.)

There are two relevant uses of så:

• As a coordinating conjunction meaning “so/therefore,” it doesn’t trigger inversion: …, så hun venter …
• As a sentence-initial adverb meaning “then/so,” it does trigger V2 inversion: Hun er syk. Så venter hun på venterommet.

Your sentence uses the coordinating conjunction, so the subject comes right after så.

In Bokmål, skulder is usually masculine:

• en skulder – skulderen – skuldre/skuldrer – skuldrene

There is also an accepted feminine form in Bokmål (more common in Nynorsk and some dialects):

• ei skulder – skuldra – skuldrer – skuldrene

So both skulderen (masc. definite singular) and skuldra (fem. definite singular) can be correct, depending on your variety.

Yes, it’s fine and natural. If you want to avoid the repetition stylistically, you could say:

• Hun sitter på venterommet og venter.
• Hun oppholder seg på venterommet mens hun venter.

• syk = ill/sick (a clear statement of being ill)
• dårlig = unwell/bad (broader, could mean “feeling bad,” not necessarily ill)

So Hun er syk i dag is stronger/more clinical than Hun er dårlig i dag. For specific symptoms, you’d use words like forkjølet (has a cold), kvalm (nauseous), svimmel (dizzy), etc.