На полке стояли уксус и майонез, а я долго думала, что добавить в салат.

Because they form a compound subject: уксус и майонез = vinegar and mayonnaise.

In Russian, when two singular nouns are joined by и and together act as the subject, the verb is usually plural:

• уксус и майонез стояли = vinegar and mayonnaise were standing

So even though each noun is singular by itself, together they require стояли, not стоял.

Russian often prefers a more specific verb of position instead of a general verb like to be.

• стоять = to stand
• лежать = to lie
• висеть = to hang

So На полке стояли уксус и майонез literally suggests that the vinegar and mayonnaise were standing on the shelf. In natural English we might simply say there were vinegar and mayonnaise on the shelf, but Russian often describes the physical position.

Also, even though уксус and майонез are technically substances, the sentence really refers to their containers (a bottle of vinegar, a jar/tube of mayonnaise), and those containers are thought of as standing.

На полке is in the prepositional case.

Here:

• на = on
• полке = prepositional singular of полка (shelf)

Russian uses на + prepositional to show location:

• на столе = on the table
• на полке = on the shelf

So На полке answers where?

If there were movement onto the shelf, Russian would use на + accusative instead:

• на полку = onto the shelf

In the past tense, Russian verbs agree with the subject in gender and number.

• думал = he / a male speaker was thinking
• думала = she / a female speaker was thinking
• думало = it was thinking
• думали = they were thinking

So я долго думала tells us that the speaker is female.

A male speaker would say:

• я долго думал

Долго means for a long time, so it fits naturally with verbs describing an action that lasts.

• я долго думала = I thought for a long time

By contrast, много usually means a lot / much / many, and with думать it would mean something more like thinking a lot in general, not specifically for a long time in this situation.

So here долго is the natural choice because the sentence is about the length of time spent deciding.

Here что means what and introduces an indirect question:

• я думала, что добавить в салат = I was thinking what to add to the salad

This is not the same as что meaning that in a statement like:

• я знаю, что он дома = I know that he is at home

So in this sentence, что добавить means what to add.

Добавить is the perfective infinitive, while добавлять is imperfective.

Here the speaker is deciding about one completed action:

• what to add to the salad
• which thing to choose and put in

That is why добавить is natural. It focuses on the action as a single whole result.

Compare:

• что добавить в салат = what to add to the salad
• добавлять в салат майонез = to add mayonnaise to salad regularly / in general / as a process

So the perfective infinitive is used because the speaker is thinking about a specific choice that will lead to a completed result.

Because в салат uses the accusative case and means into the salad.

Russian uses:

• в + accusative for direction / destination
• в + prepositional for location

So:

• добавить в салат = to add into the salad
• в салате = in the salad

Here the idea is movement or insertion of an ingredient into the salad, so Russian uses в салат.

They are in the nominative case because they are the subject of the verb стояли.

• уксус = nominative singular
• майонез = nominative singular

Even though the verb is plural, each noun itself stays in the nominative singular because each names one item in the compound subject.

А often shows a contrast, switch of focus, or a new piece of information set against what came before.

Here the sentence has two parts:

• На полке стояли уксус и майонез
• а я долго думала, что добавить в салат

The first part describes the situation. The second shifts to the speaker’s reaction or dilemma. So а works well because it means something like:

• and meanwhile
• whereas
• while
• sometimes even a light but

Using и would simply connect the events. Using а makes the contrast or scene shift clearer.

Russian word order is flexible, and speakers often put the setting first.

• На полке стояли уксус и майонез puts emphasis first on where the items were.
• Уксус и майонез стояли на полке starts with the items themselves.

Both are grammatical, but the original version sounds natural because it first establishes the scene: on the shelf.

This kind of word order is very common in Russian narrative style.

Literally the words mean the substances:

• уксус = vinegar
• майонез = mayonnaise

But in everyday Russian, just like in English, the noun can stand for the container/product:

• На столе стояло молоко = There was milk on the table
  often meaning a carton or bottle of milk

So here уксус и майонез стояли is naturally understood as something like the vinegar bottle and the mayonnaise jar/tube were on the shelf.

Yes. Russian often leaves out a subject when it is understood from context.

In что добавить в салат, the understood subject is basically I:

• я думала, что добавить в салат
• literally: I was thinking what [for me] to add to the salad

Russian infinitive constructions often work this way after verbs like знать, решать, думать, понимать:

• не знаю, что сказать = I don’t know what to say
• решил, куда пойти = he decided where to go

So this is a very common and natural pattern.