Learn Hardcore Russian: По выходным мой дедушка возит внука в парк. - On weekends my grandfather drives his grandson to the park.

Some masculine Russian nouns referring to males end in -а or -я. They decline like many feminine-looking nouns, but they are still grammatically masculine.

Examples:

дедушка = grandfather
папа = dad
дядя = uncle
мужчина = man

So мой дедушка is correct, not моя дедушка, because the noun is masculine in meaning and agreement.

Why is it внука and not внук?

Because внука is the accusative case, and внук is an animate masculine noun.

In Russian, masculine animate nouns have:

nominative: внук
accusative: внука

Here, the grandson is the direct object of возит, so Russian uses the accusative:

дедушка возит внука = grandfather takes/drives his grandson

This is a very important pattern:

Я вижу брата
Он знает учителя
Мы любим кота

For animate masculine nouns, accusative usually looks like genitive.

Why is it в парк and not в парке?

Because this sentence describes movement toward a place.

With в:

в + accusative = into / to
в + prepositional = in / inside

So:

в парк = to the park (direction)
в парке = in the park (location)

Compare:

Дедушка идёт в парк. = He is going to the park.
Дедушка гуляет в парке. = He is walking in the park.

Why is the verb возит used here?

возить means to transport / take someone or something regularly, repeatedly, or back and forth, usually by some means of transport.

So возит here suggests a habitual action:

По выходным мой дедушка возит внука в парк.
On weekends, my grandfather takes/drives his grandson to the park.

This is different from a one-time trip.

What is the difference between возит and везёт?

This is a classic Russian verb pair.

возить = to transport repeatedly / habitually / in various directions
везти = to be transporting right now / in one конкретe trip / in one direction

So:

Дедушка возит внука в парк по выходным.
= He takes him there regularly.
Сейчас дедушка везёт внука в парк.
= Right now he is taking him to the park.

In your sentence, the idea is habitual, so возит is the natural choice.

Does возит mean they go by car?

Usually it suggests transporting someone by vehicle or at least not on foot.

For example, it can imply going:

by car
by bus
by train
by some other transport

If you specifically wanted takes on foot / leads, Russian would more likely use водит in some contexts:

водить ребёнка в парк = to take a child to the park regularly

So возит often gives the feeling that the grandfather is driving or otherwise transporting the grandson.

Why is there no word for the in this sentence?

Because Russian does not have articles like a or the.

So:

дедушка can mean a grandfather, the grandfather, or grandfather, depending on context
внука can mean a grandson, the grandson, or his grandson, depending on context

In this sentence, English naturally uses my grandfather and his grandson / the grandson, but Russian expresses that without articles.

The possessive мой helps make the subject specific:

мой дедушка = my grandfather

Is мой necessary here?

Not always.

Russian often omits possessives when the relationship is obvious from context. So in some situations, you could hear:

По выходным дедушка возит внука в парк.

That could still mean Grandpa takes his grandson to the park on weekends.

But мой дедушка makes it explicit that the speaker is talking about my grandfather, so it sounds natural and clear.

Can the word order be changed?

Yes. Russian word order is flexible because case endings show the grammatical roles.

The neutral order here is:

По выходным мой дедушка возит внука в парк.

But you could also say things like:

Мой дедушка по выходным возит внука в парк.
Внука мой дедушка по выходным возит в парк.
В парк мой дедушка возит внука по выходным.

These all keep roughly the same basic meaning, but the emphasis changes.

For learners, the original sentence is a very natural neutral version.

Is this sentence talking about one weekend or a repeated habit?

A repeated habit.

Two things show that:

по выходным = on weekends / every weekend
возит is the imperfective habitual verb

So the meaning is not this weekend my grandfather is taking his grandson to the park, but rather:

My grandfather takes his grandson to the park on weekends.

What case is мой дедушка in?

It is in the nominative case, because it is the subject of the sentence.

The subject is the person doing the action:

мой дедушка = the one who takes/drives

So the cases in the sentence are:

по выходным = dative plural
мой дедушка = nominative
внука = accusative
в парк = accusative after a motion preposition

This is a good sentence for seeing several common Russian case patterns at once.