На столе стоит банка белой краски.

Because this sentence describes location, not motion.

• на столе = on the table (where?)
• на стол = onto the table (to where?)

After на, Russian uses:

• Prepositional case for location: на столе
• Accusative case for movement toward a place: на стол

So:

• На столе стоит банка = A jar is standing on the table.
• Банку поставили на стол = They put the jar onto the table.

Столе is the prepositional singular of стол.

The basic form is:

• стол = table

After на when it means in/on/at a place, Russian often uses the prepositional case:

• на столе = on the table
• в доме = in the house
• на улице = on the street / outside

So here:

• На столе = On the table

Russian often omits to be in the present tense, but here стоит is not just is. It has its own meaning: is standing.

So this sentence is more literally:

• На столе стоит банка белой краски.
• A jar of white paint is standing on the table.

Russian commonly uses verbs of position:

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

A jar is thought of as something upright, so стоит is natural.

You could hear:

• На столе банка белой краски.

That is possible in some contexts and means something like There is a jar of white paint on the table, but стоит is more natural if you want to describe its position specifically.

Because Russian often chooses the verb based on the object's physical position.

• стоит = stands upright
• лежит = lies horizontally

A банка is normally imagined as upright on its base, so Russian says:

• банка стоит

If the jar were on its side, then лежит could make sense:

• На столе лежит банка.
  = The jar is lying on the table.

So the choice reflects how the object is positioned, not just the fact that it exists.

Because банка is the subject of the sentence.

The sentence structure is basically:

• банка стоит = the jar stands / is standing

So банка is in the nominative singular, the dictionary form.

Even though the sentence starts with На столе, that phrase is just the location. The real grammatical subject is still банка.

This is a very common Russian pattern: container + contents in the genitive.

So:

• банка краски = a jar of paint
• стакан воды = a glass of water
• чашка чая = a cup of tea
• бутылка молока = a bottle of milk

Here краски is in the genitive singular because it means paint as the substance inside the jar.

So:

• банка белой краски = a jar of white paint

Because краска here means paint as a material/substance, and after a container noun like банка, Russian usually puts the substance in the genitive.

• краска = paint
• краски = of paint

This is singular genitive, not plural.

Why singular? Because we are talking about paint as a mass noun, not several different paints.

Compare:

• банка краски = a jar of paint
• магазин красок = a store of paints / paint products

So in your sentence, краски means of paint, not paints.

Because белой has to match краски, and краски is in the genitive singular.

The noun is:

• краска = paint

In this sentence it becomes:

• краски = of paint

So the adjective must also become genitive singular feminine:

• белая краска = white paint
• белой краски = of white paint

This is normal adjective agreement in Russian:

• adjective and noun agree in gender
• number
• case

So:

• банка белой краски = a jar of white paint

The ending -ой shows that белой is:

• feminine
• singular
• genitive (also the same form as feminine singular dative/instrumental/prepositional in some patterns, but here the function is genitive)

Since краска is feminine, singular, and in the genitive, the adjective must match it.

Compare:

• белая краска = white paint (nominative)
• нет белой краски = there is no white paint (genitive)
• банка белой краски = a jar of white paint (genitive)

So -ой is just the adjective agreement ending required by краски.

Both word orders are possible, but Russian word order is flexible and often depends on focus.

• На столе стоит банка белой краски.
  This presents the location first: On the table, there is a jar of white paint.
• Банка белой краски стоит на столе.
  This puts more focus on the jar itself.

Starting with the place is very natural in Russian when introducing something in a scene.

So this sentence sounds like:

• On the table stands a jar of white paint.

It is not poetic here; it is a normal Russian way to structure information.

Yes, it is singular in Russian too.

Russian краска can mean:

• paint as a material/substance
• sometimes a kind/type of paint, depending on context

In банка белой краски, it behaves like a substance noun, similar to English paint, water, or milk.

So although English does not usually mark this with a singular ending, Russian still treats it as a singular noun here:

• краска → краски in the genitive singular

A natural stress pattern is:

• На столе́ стои́т ба́нка бе́лой кра́ски.

Main stresses:

• столе́
• стои́т
• ба́нка
• бе́лой
• кра́ски

This can help because the written form does not show stress marks in normal Russian spelling.

Usually, есть would not be the most natural choice in this sentence.

• На столе стоит банка белой краски. = natural; describes where the jar is and how it is positioned.
• На столе есть банка белой краски. = possible in some contexts, but less natural here; it emphasizes existence more than position.

In everyday Russian, when talking about where objects are, speakers often prefer:

• no verb at all, or
• a positional verb like стоит, лежит, висит

So стоит is the most idiomatic choice here.