Когда мы едем на дачу, мы везём еду в машине и не носим тяжёлые пакеты в руках.

Because ехать means to go / travel by vehicle, while идти means to go on foot.

So:

• мы едем на дачу = we are going to the dacha by some vehicle
• мы идём на дачу = we are walking to the dacha

Since the sentence later mentions в машине (in the car), едем is the natural choice.

They are related, but they focus on different things.

• едем comes from ехать = to go / ride / travel by vehicle
• везём comes from везти = to transport / carry something by vehicle

So in this sentence:

• мы едем на дачу = we are going to the dacha
• мы везём еду = we are taking food with us / transporting food

A useful way to remember it:

• ехать = the people themselves are traveling
• везти = they are taking something along in a vehicle

This is just the normal Russian idiom: people say ехать на дачу, быть на даче, жить на даче.

Even though in English we might think of it as to the dacha / into the house, Russian treats дача more like a destination area or country property, so на is used.

Compare:

• на дачу = to the dacha
• на даче = at the dacha

Using в дачу would usually sound wrong in this meaning.

Both are possible in Russian, but they mean different things.

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

In your sentence, the idea is that the food is physically located inside the car:

• мы везём еду в машине = we transport the food in the car

If you said на машине, it would emphasize the means of transport:

• мы едем на дачу на машине = we go to the dacha by car

So в машине is about location, while на машине is about method.

Because еду can mean two different things:

1. еду = accusative singular of еда (food)
2. еду = I am going / riding from ехать

They are spelled the same, so context tells you which one it is.

In this sentence:

• мы везём еду = we are transporting food

After везём, a direct object is expected, so еду clearly means food.

Носить means to carry, usually by hand, on your body, or in repeated/ongoing situations.

Here:

• не носим тяжёлые пакеты в руках = we don’t carry heavy bags in our hands

That contrasts nicely with везём:

• везём еду в машине = we move it by car
• не носим ... в руках = we don’t carry it by hand

So the sentence is contrasting two ways of moving things:

• by vehicle
• by hand

Russian normally uses the plural here:

• в руках = in (one’s) hands / by hand

This is the standard expression. Even when referring to one person, Russian often says в руках because people normally have two hands.

Examples:

• держать в руках = to hold in one’s hands
• нести в руках = to carry in one’s hands

So в руках is just the natural idiomatic wording.

Russian often leaves out possessives like my, your, our when they are obvious from context.

So:

• в машине can mean in the car or in our car, depending on context
• в руках can mean in our hands

Because the subject is already мы (we), it is clear whose hands are meant. Russian prefers not to repeat that information unless it needs emphasis.

If you really wanted to specify it, you could say:

• в нашей машине
• в наших руках

But in this sentence that would sound unnecessary.

It is a direct object, so it is in the accusative plural. But for inanimate nouns in Russian, the accusative plural is usually the same as the nominative plural.

So:

• nominative plural: тяжёлые пакеты
• accusative plural: тяжёлые пакеты

That is why it looks unchanged.

If it were an animate noun, the accusative plural would look different.

In Russian, the present tense of an imperfective verb can describe:

• what is happening now
• what generally happens
• what happens whenever a situation occurs

Here the sentence has a general/habitual meaning:

• Когда мы едем на дачу, ... = When/Whenever we go to the dacha, ...

So the present tense is completely normal.

This is similar to English sentences like:

• When we go there, we take food in the car.

Because когда means when, and here it introduces a situation that regularly happens.

• Когда мы едем на дачу, ... = When/Whenever we go to the dacha, ...

If you used если, the meaning would become more conditional:

• Если мы едем на дачу, ... = If we are going to the dacha, ...

That sounds more like a condition or possibility.
Когда fits better if the speaker means a normal repeated situation.

Yes, they are all imperfective forms.

• едем ← ехать
• везём ← везти
• носим ← носить

Imperfective is used here because the sentence describes an ongoing or repeated situation, not a single completed action.

That is why the sentence feels like:

• When we go to the dacha, we take food in the car and don’t carry heavy bags in our hands.

If Russian wanted to focus on completion, it would usually use perfective verbs in a different structure, often referring to a specific event.

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

The original order is neutral and natural:

• Когда мы едем на дачу, мы везём еду в машине и не носим тяжёлые пакеты в руках.

You could move parts around for emphasis, for example:

• Когда мы едем на дачу, еду мы везём в машине...
• ...и тяжёлые пакеты в руках не носим.

But those versions sound more marked or emphatic. For a learner, the original word order is the best standard model.

Because тяжёлые is an adjective agreeing with пакеты.

Since пакеты is:

• plural
• masculine in singular, but that does not matter here because plural has its own form
• accusative plural in this sentence

the adjective must also be in the matching plural form:

• тяжёлые пакеты = heavy bags

For inanimate plural nouns, nominative and accusative are the same, so the adjective also looks the same in both cases.

The sentence contrasts transporting by car with carrying by hand.

• везём еду в машине = we take the food in the car
• не носим тяжёлые пакеты в руках = we don’t carry heavy bags in our hands

So the grammar and vocabulary work together to show:

• going by vehicle
• bringing things with you by vehicle
• avoiding manual carrying

This is a very typical Russian way to use motion verbs precisely.