Мы взяли тележку, потому что чемодан и коробка были слишком тяжёлыми.

Взяли is the past tense plural form of взять.

• взять = to take
• взяли = we/they took

It is also perfective, which means the action is viewed as completed: we took/got a cart.
A learner may compare it with брали from брать:

• мы взяли тележку = we took/got a cart
• мы брали тележку = we were taking / used to take / took (with an imperfective viewpoint)

Here, взяли fits well because the sentence describes a completed action.

Because it is the direct object of the verb взяли.

The noun тележка is feminine, and feminine nouns ending in -а usually change like this in the singular:

• nominative: тележка
• accusative: тележку

So:

• Мы взяли тележку = We took a cart

This is a very common pattern:

• книга → книгу
• машина → машину
• коробка → коробку

Yes, Russian often can leave it out.

Because взяли already shows plural past tense, the sentence could also be:

• Взяли тележку, потому что чемодан и коробка были слишком тяжёлыми.

But adding мы makes the subject explicit. It can sound clearer, more natural in context, or slightly more emphatic.

So both are possible, but мы is not strange or unnecessary.

Because they are the subject of the clause чемодан и коробка были слишком тяжёлыми.

Subjects normally stand in the nominative case, which is the dictionary form:

• чемодан = suitcase
• коробка = box

Together they form a compound subject:

• чемодан и коробка = the suitcase and the box

So they stay in nominative.

Because the subject is plural.

Even though чемодан is masculine singular and коробка is feminine singular, together they mean two things, so Russian uses the plural:

• чемодан и коробка были... = the suitcase and the box were...

Compare:

• чемодан был тяжёлым = the suitcase was heavy
• коробка была тяжёлой = the box was heavy
• чемодан и коробка были тяжёлыми = the suitcase and the box were heavy

This is a very good question, because both forms may be seen after быть.

In this sentence, тяжёлыми is the instrumental plural form of тяжёлый.

It agrees with чемодан и коробка, which are plural as a combined subject:

• masculine singular: тяжёлый
• feminine singular: тяжёлая
• plural nominative: тяжёлые
• plural instrumental: тяжёлыми

After forms of быть, Russian often uses the instrumental for the predicate part, especially when describing a state or condition:

• Он был уставшим.
• Они были счастливыми.
• Чемодан и коробка были слишком тяжёлыми.

You may also hear были слишком тяжёлые. That is possible too.
Very roughly:

• тяжёлыми can sound a bit more like they were in a heavy state / they turned out to be too heavy
• тяжёлые can sound a bit more direct and neutral in some contexts

In modern Russian, both can occur, but тяжёлыми is perfectly normal here.

Слишком means too in the sense of excessively.

So:

• слишком тяжёлыми = too heavy

This is different from очень:

• очень тяжёлые = very heavy
• слишком тяжёлые = too heavy

So the idea is not just that the suitcase and box were heavy, but that they were more heavy than was manageable or convenient, which is why a cart was needed.

Потому что means because.

It introduces the reason:

• Мы взяли тележку = We took a cart
• потому что чемодан и коробка были слишком тяжёлыми = because the suitcase and the box were too heavy

The comma is used because потому что introduces a subordinate clause. In Russian, this comma is normally required:

• ..., потому что ...

So the punctuation is standard and important.

No, Russian word order is fairly flexible.

The given version is natural:

• Мы взяли тележку, потому что чемодан и коробка были слишком тяжёлыми.

But Russian can move things around for emphasis. For example:

• Потому что чемодан и коробка были слишком тяжёлыми, мы взяли тележку.

This still means the same thing: Because the suitcase and the box were too heavy, we took a cart.

However, not every order sounds equally natural in every context. The original sentence is a very normal, neutral way to say it.

Russian has no articles like a/an/the.

So:

• тележку can mean a cart or the cart
• чемодан can mean a suitcase or the suitcase
• коробка can mean a box or the box

Context tells you which is meant.

In this sentence, English might translate it either way depending on the situation:

• We took a cart because the suitcase and the box were too heavy
• We took the cart because the suitcase and the box were too heavy

Russian leaves that choice to context rather than using articles.