У бабушки на полке стоит старая ваза из мастерской, а рядом — маленькая рамка с нашим фото.

Not literally. In this sentence, у бабушки means something like at grandmother’s place or with grandmother.

Russian often uses у + Genitive to show where something is, especially in the sense of someone’s home, space, or possession. So у бабушки на полке means on the shelf at Grandma’s place.

It does not mean the vase is physically standing next to the grandmother.

Because the preposition у requires the Genitive.

The base form is бабушка, but after у it becomes у бабушки.

This is a very common pattern:

• у мамы
• у друга
• у учителя

It often expresses:

• location near/at someone
• possession, as in у меня есть...

Because this sentence describes location, not movement.

• на полке = on the shelf → location, so Russian uses the Prepositional
• на полку = onto the shelf → direction/movement, so Russian uses the Accusative

Compare:

• Ваза стоит на полке. = The vase is on the shelf.
• Я ставлю вазу на полку. = I put the vase onto the shelf.

Russian often prefers a positional verb instead of a general is when talking about where something is located.

Here стоит is used because the vase is thought of as being in an upright position.

Common Russian location verbs include:

• стоит = stands
• лежит = lies
• висит = hangs

So:

• a vase on a shelf often стоит
• a book on a table may лежит
• a picture on a wall висит

This is more natural in Russian than using a general present-tense to be, which is usually omitted.

Usually not if you want this natural descriptive effect.

In present-tense Russian, есть is not normally used like English is for simple location. Instead, Russian often:

• omits the verb entirely, or
• uses a more specific positional verb like стоит, лежит, or висит

So на полке стоит старая ваза sounds natural because it tells you both that the vase is there and how it is positioned.

Because it is the subject of the clause.

The noun is ваза, and the adjective старая agrees with it:

• feminine
• singular
• nominative

So:

• старая ваза = feminine singular nominative

The same thing happens in маленькая рамка later in the sentence.

The preposition из takes the Genitive, so мастерская becomes мастерской.

Here из мастерской means the vase is from a workshop/studio. It shows origin or source.

So this phrase describes the vase as one that came from some workshop or studio, rather than just describing where it is now.

The verb is omitted because it is understood from the first part of the sentence.

The full idea is essentially:

• У бабушки на полке стоит старая ваза из мастерской, а рядом стоит маленькая рамка с нашим фото.

In Russian, it is very common to leave out repeated words when they are obvious. The dash helps mark that omission and creates a natural pause.

So the second part means:

• and next to it, a small frame with our photo

with the idea of stands/is there understood.

Because а often links two things by setting them side by side.

It does not always mean strong contrast. Very often it simply means something like:

• and meanwhile
• and as for this other thing
• while
• and next to it

Here it works well because the sentence is describing two nearby objects in relation to each other:

• one thing on the shelf is a vase,
• and next to it there is a small frame.

Using и would be possible in some contexts, but а sounds very natural for this kind of visual description.

It is governed by с in the meaning with, which takes the Instrumental case.

That is why the adjective changes:

• наш → нашим

So:

• с нашим фото = with our photo

The noun фото does not change its form, but the adjective shows the case clearly.

Because фото is an indeclinable noun in modern Russian.

That means its form stays the same in different cases. The case is shown by:

• the preposition
• any agreeing adjective or pronoun

So in с нашим фото:

• с tells you Instrumental is needed
• нашим shows Instrumental, neuter, singular
• фото stays фото

This is common with some borrowed nouns in Russian.

Russian word order is flexible, and this order is very natural for description.

The sentence starts with the setting:

• У бабушки на полке

Then it introduces what is there:

• стоит старая ваза...

Then it adds another nearby object:

• а рядом — маленькая рамка...

This kind of order helps the listener imagine the scene step by step. English often does something similar in descriptive writing, but Russian uses this especially freely because case endings make the relationships clear.