На торте была белая глазурь и немного орехов.

Because на means on, and after на when you are talking about location, Russian uses the prepositional case.

So:

• торт = cake
• на торте = on the cake

The ending changes from -т to -те because торт becomes prepositional singular.

If you were talking about something inside the cake, you would normally use в instead:

• в торте = in the cake

Because белая describes глазурь, and Russian adjectives must agree with the noun they describe in:

• gender
• number
• case

Here, глазурь is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• белый = white (dictionary form, masculine)
• белая глазурь = white icing

A noun ending in -ь can be either masculine or feminine in Russian. You cannot tell the gender from -ь alone; you often have to learn it with the word.

Глазурь is a feminine noun, so it takes feminine forms like:

• белая глазурь
• глазурь была

This is a normal pattern for many feminine nouns of the so-called third declension.

Была is the past tense, feminine singular form of быть (to be).

It is feminine singular because it agrees with глазурь, which is feminine singular.

So:

• он был = he/it was
• она была = she/it was
• они были = they were

Here the sentence is presenting what was on the cake, and the verb matches глазурь.

This is a very common learner question.

In a sentence like На торте была белая глазурь и немного орехов, Russian is using a kind of presentational/existential structure: it is introducing what was on the cake.

In this type of sentence, especially when the verb comes before the nouns, Russian often uses a singular verb that agrees with the first noun phrase. Here that first noun phrase is белая глазурь, which is feminine singular, so была sounds natural.

Also, немного орехов is a quantity expression, not a simple plain plural noun, which makes singular agreement even less surprising.

If you reorganize the sentence and put the whole subject first, then plural agreement becomes more expected:

• Белая глазурь и немного орехов были на торте.

So была here is natural because of both:

1. the word order
2. the fact that немного орехов is a quantity phrase

Because after немного (a little / some), Russian normally uses the genitive plural of the noun.

So:

• орехи = nuts
• орехов = of nuts / nuts (after a quantity word)

This is the standard pattern after words like:

• много = many/a lot of
• мало = few/little
• немного = a little/some
• сколько = how many/how much

Examples:

• много орехов = many nuts
• мало времени = little time
• немного сахара = a little sugar

In meaning, it is plural: it means some nuts.

But grammatically, it behaves as a quantity phrase, and that is why it does not always act exactly like an ordinary plural noun phrase.

That is why learners sometimes get confused about verb agreement in sentences like this. Russian is not simply treating it the same way as plain орехи.

Compare:

• На столе были орехи. = There were nuts on the table.
• На столе было немного орехов. = There were a few nuts on the table.

The second sentence often uses singular было because the phrase is built around a quantity expression.

Russian does not need a dummy subject like English there.

English says:

• There was white icing on the cake.

Russian can simply say:

• На торте была белая глазурь.

Literally, that is closer to:

• On the cake was white icing.

But in natural English translation, it often becomes:

• There was white icing on the cake.

So the idea of there was is expressed by the structure of the sentence, not by a separate word meaning there.

Because Russian word order is flexible, and starting with На торте sets the scene first.

It is like saying:

• As for the cake / On the cake, there was...

This is very natural when you are describing what was present somewhere.

If you change the order, the emphasis changes:

• На торте была белая глазурь и немного орехов.
  Focus: what was on the cake

• Белая глазурь и немного орехов были на торте.
  Focus: the icing and nuts themselves

Both are possible, but the original version sounds very natural for introducing details in a description.

Yes. In the present tense, Russian usually omits the verb to be.

So the present-tense version would normally be:

• На торте белая глазурь и немного орехов.

That means:

• There is white icing and some nuts on the cake.

But in the past tense, Russian does use forms of быть, so you get:

• На торте была белая глазурь и немного орехов.

You know it from context, because Russian has no articles like a or the.

So:

• торт can mean a cake or the cake
• глазурь can mean icing, the icing, or sometimes just some icing, depending on context

That is normal in Russian. The language usually leaves this unstated unless it really needs to be clarified.