Meine Enkelin stellt dieselbe Vase jedes Jahr an denselben Platz.

Because German often uses different put/place verbs depending on the object's final position.

• stellen = put something so that it ends up standing upright
• legen = put something so that it ends up lying flat
• setzen = put someone/something into a sitting position

A vase normally stands upright, so stellen is the natural choice.

Compare:

• Sie stellt die Vase auf den Tisch. = She puts the vase on the table.
• Die Vase steht auf dem Tisch. = The vase is standing on the table.

So stellt is the action of placing it there.

Yes, derselbe / dieselbe / dasselbe is written as one word.

It means the very same one or one and the same. In your sentence, it means the granddaughter places the identical vase there every year.

A useful contrast:

• dieselbe Vase = the exact same vase
• die gleiche Vase = a vase of the same kind/type, or an identical-looking one

In everyday speech, native speakers do sometimes blur this distinction, but in careful German, dieselbe means the same actual object.

Because the two noun phrases have different gender and different case.

• Vase is feminine
• Platz is masculine

Also:

• dieselbe Vase is the direct object of stellt, so it is in the accusative
• denselben Platz comes after an and shows a destination, so it is also accusative

The forms are:

• feminine accusative singular: dieselbe
• masculine accusative singular: denselben

So the endings are not random; they reflect the grammar.

Here an means something like to or at a particular spot/position.

With places, German often uses an for being placed at a specific point, edge, or location. In this sentence, an denselben Platz means to the same spot/place.

It is just the natural preposition for this idea in German. English and German do not always choose the same preposition.

Because an is a two-way preposition.

Two-way prepositions take:

• accusative when there is movement toward a destination
• dative when there is location without movement

Here, the vase is being moved to that spot, so German uses accusative:

• an denselben Platz = to the same place

If you were only describing where the vase is, you would use dative:

• Die Vase steht an demselben Platz. = The vase is in the same place.

So:

• stellt ... an denselben Platz = puts ... to that place
• steht ... an demselben Platz = is standing at that place

Jedes Jahr is an accusative adverbial of time.

German often expresses time phrases like this without a preposition:

• jeden Tag = every day
• jede Woche = every week
• jeden Monat = every month
• jedes Jahr = every year

So the sentence does not need a word like in or during here. A bare accusative time expression is completely normal.

Because Jahr is a neuter noun.

The form of jeder changes with gender and case:

• masculine accusative: jeden
• feminine accusative: jede
• neuter accusative: jedes

Since Jahr is neuter, the correct form is:

• jedes Jahr

Compare:

• jeden Tag — Tag is masculine
• jede Woche — Woche is feminine
• jedes Jahr — Jahr is neuter

The sentence follows normal main-clause German word order:

• Meine Enkelin = subject
• stellt = finite verb in second position
• dieselbe Vase = direct object
• jedes Jahr = time expression
• an denselben Platz = place/destination expression

A rough pattern is:

Subject + verb + object + time + place

German main clauses require the finite verb to be in position 2, but the other elements are fairly flexible.

Yes. German is quite flexible as long as the verb stays in the right place.

For example, you can also say:

• Jedes Jahr stellt meine Enkelin dieselbe Vase an denselben Platz.

This puts more emphasis on every year.

You may also hear:

• Meine Enkelin stellt jedes Jahr dieselbe Vase an denselben Platz.

That is also natural.

So the original order is normal, but it is not the only possible order.

Meine Enkelin is the subject, so it is in the nominative case.

• Enkelin is feminine singular
• the possessive determiner mein therefore becomes meine in the nominative feminine singular

So:

• meine Enkelin = my granddaughter

If the noun were masculine, the form would be different:

• mein Enkel = my grandson

You could, but it would not mean exactly the same thing.

• diese Vase = this vase
• dieselbe Vase = the same vase, the identical vase

So diese Vase would simply point to a vase, while dieselbe Vase specifically tells us that it is the same one every year.

That distinction matters in this sentence.