Ich muss noch Salz in die Suppe hineingeben.

This is because German is using a modal verb: müssen = must / have to.

With a modal verb:

• the conjugated modal goes in the normal verb position
• the main verb stays in the infinitive at the end

So:

• Ich muss ... hineingeben
• literally: I must ... put in

This is very common in German:

• Ich will gehen. = I want to go.
• Sie kann schwimmen. = She can swim.

Here, muss is the finite verb, and hineingeben is the infinitive.

Here noch means something like:

• still
• yet
• one more thing
• in addition

So Ich muss noch Salz in die Suppe hineingeben means:

• I still have to add salt to the soup
• I need to add some more salt to the soup

In this sentence, noch suggests that this action has not been done yet, but it still needs to happen.

Compare:

• Ich muss Salz in die Suppe geben. = I have to add salt to the soup.
• Ich muss noch Salz in die Suppe geben. = I still have to add salt / I have to add some more salt.

Because German uses different cases after in depending on whether you mean:

• location → dative
• direction/movement into something → accusative

Here, the salt is being put into the soup, so there is a sense of movement/direction. That is why German uses the accusative:

• in die Suppe = into the soup

If you were describing location, you would use dative:

• Das Salz ist in der Suppe. = The salt is in the soup.

So:

• in die Suppe geben = put into the soup
• in der Suppe sein = be in the soup

Hineingeben means to put in, to add in, or to put into.

It is made up of:

• geben = to give
• hinein = in / into there

In cooking, hineingeben is a very natural verb for adding an ingredient into something.

So:

• Salz in die Suppe hineingeben = add salt into the soup

It is a bit more explicit than just geben, because it clearly expresses movement into something.

Yes, absolutely.

Ich muss noch Salz in die Suppe geben is perfectly correct and very natural.

Adding hinein makes the idea of into the soup a little more explicit, but in many contexts German speakers leave it out because in die Suppe already makes the direction clear.

So both work:

• Ich muss noch Salz in die Suppe geben.
• Ich muss noch Salz in die Suppe hineingeben.

The version with hinein can sound a bit more specific or a bit more vivid, but the basic meaning is the same.

Yes. Hineingeben is treated as a separable verb.

In a main clause with a simple tense, the prefix part often separates and goes to the end:

• Ich gebe noch Salz in die Suppe hinein.

But when the verb is in the infinitive, as it is here after muss, it stays together:

• Ich muss noch Salz in die Suppe hineingeben.

So:

• finite main verb: Ich gebe ... hinein
• infinitive with modal: Ich muss ... hineingeben

That is why you see the full form hineingeben at the end.

Because Salz is being used as a mass noun here, like water, sugar, or rice in English.

When German talks about an unspecified amount of a substance, it often uses no article:

• Ich brauche Wasser.
• Wir kaufen Zucker.
• Er gibt Salz in die Suppe.

So Salz here means some salt, not the salt or a salt.

If you wanted to be more specific, you could add something:

• das Salz = the salt
• etwas Salz = some salt
• ein bisschen Salz = a little salt

Because German main clauses normally follow the V2 rule: the finite verb goes in second position.

Here the sentence begins with Ich, so the finite verb muss comes right after it:

• Ich muss noch Salz in die Suppe hineingeben.

This is standard German word order.

If something else came first, the verb would still stay second:

• Jetzt muss ich noch Salz in die Suppe hineingeben.
• In die Suppe muss ich noch Salz hineingeben.

The key point is that the conjugated verb stays in second position.

This is about the speaker’s point of view.

• hinein = into there, away from the speaker’s viewpoint
• herein = into here, toward the speaker’s viewpoint

In many everyday sentences, especially with things like soup or a bowl, German speakers often use hinein because the focus is just on movement into something.

For example:

• Er geht ins Haus hinein. = He goes into the house.
• Komm herein! = Come in!
  Here herein is natural because the movement is toward the speaker.

In your sentence, hineingeben is the normal choice.

Yes, noch can move, but its position affects what it sounds like it modifies.

In your sentence:

• Ich muss noch Salz in die Suppe hineingeben.

this sounds like I still have to add salt or I have to add some more salt.

This is the most natural position for the intended meaning.

Other placements are possible, but they may sound different or more marked. For example:

• Ich muss Salz noch in die Suppe hineingeben.
  This is much less natural in ordinary speech.

So as a learner, the safest pattern is:

• subject + modal + noch + object + other elements + infinitive

That gives you a very natural sentence here.

Yes, they can, and it is correct. In recipes and kitchen contexts, German often uses verbs like:

• hineingeben = add in
• dazugeben = add
• geben = put/add
• einrühren = stir in

Depending on style, you might also hear:

• Ich muss noch Salz in die Suppe geben.
• Ich muss noch Salz dazugeben.

So hineingeben is not wrong or strange. It is just one natural way to express add into.