Вчера я ездил на машине в магазин.

These three forms highlight different parts of the action:

• ездил = went by vehicle; focuses on the fact of the trip
• ехал = was going / was on the way; focuses on the movement in progress
• поехал = set off / started going; focuses on the beginning

So Вчера я ездил на машине в магазин is a natural way to say that yesterday the speaker made that trip by car.

Compare:

• Вчера я ехал в магазин, когда увидел друга.
  Yesterday I was going to the store when I saw a friend.
• Вчера я поехал в магазин в шесть.
  Yesterday I set off for the store at six.

Often, yes. In many everyday contexts, ездил can suggest a completed outing: the speaker went there and later returned.

So Вчера я ездил в магазин often feels like I went to the store yesterday as a whole event, not just I was on my way there.

That said, it is not a strict mathematical rule. Context matters. If you want to stress a single successful there-and-back trip even more strongly, Russian also often uses съездил.

Ездил is:

• past tense
• masculine
• singular

It comes from the infinitive ездить.

Russian past tense is formed with -л, and in the singular it agrees with gender:

• я ездил = I went, if the speaker is male
• я ездила = I went, if the speaker is female
• мы ездили = we went

So this sentence tells you the speaker is male, unless it is being used in some unusual context.

Russian usually expresses transport with на plus the vehicle noun:

• на машине = by car
• на автобусе = by bus
• на поезде = by train
• на такси = by taxi

This is just the normal Russian pattern. Literally it may feel like on a car, but idiomatically it means by car.

Here машине is in the prepositional singular.

The noun is машина, and after на in this transport expression, Russian uses the prepositional form:

• машина → на машине

This is worth memorizing as a common pattern: ехать / ездить на + prepositional for means of transport.

Because the meanings are different:

• на машине = by car
• в машине = in the car

So:

• Я ездил на машине. = I went by car.
• Я был в машине. = I was in the car.

A learner often expects in the car, but Russian uses на машине for the method of transport.

Because Russian distinguishes:

• motion to a place: в + accusative
• location in a place: в + prepositional

So:

• в магазин = to the store
• в магазине = in the store

In this sentence, the speaker is moving toward the store, so в магазин is correct.

Also, магазин is a masculine inanimate noun, and its accusative singular looks the same as the nominative singular. That is why you see магазин, not a changed ending.

Not necessarily.

Я ездил на машине only tells you that the trip was made by car. It does not by itself tell you whether the speaker was:

• driving
• riding as a passenger
• being driven by someone else

If you want to make it clear that the speaker drove, you could say something more specific, such as Я сам был за рулём or Я водил машину depending on the context.

Sometimes, yes, especially in conversation if the subject is obvious from context.

For example, if everyone already knows you are talking about yourself, you might hear:

• Вчера ездил на машине в магазин.

However, Russian past tense does not show person, only gender and number. So without я, the form ездил could refer to I, you, or he, depending on context. In a standalone sentence, keeping я makes everything clear.

No. Russian word order is flexible, and different orders change the emphasis more than the basic meaning.

The given sentence is a neutral, natural order:

• Вчера я ездил на машине в магазин.

You could also say:

• Я вчера ездил на машине в магазин.
• В магазин я вчера ездил на машине.
• На машине я вчера ездил в магазин.

All of these are possible, but each one highlights a different part of the sentence. Russian uses word order for focus much more than English does.

Because Russian has no articles.

So магазин can mean:

• a store
• the store

The context tells you which one is meant. English needs articles, but Russian does not. That is why в магазин can correspond to either to a store or to the store, depending on the situation.