Даже если я очень спешу утром, я всё равно беру с собой банан или грушу.

They work together.

• даже если = even if
• всё равно = still / anyway / all the same

So the structure is:

Даже если X, я всё равно Y
= Even if X, I still Y

This pairing is very common in Russian. You can omit всё равно, but then the sentence sounds a little less emphatic.

Спешу is the 1st person singular present tense of спешить.

So:

• я спешу = I am hurrying / I’m in a hurry

In this sentence, it describes a repeated or typical situation: when I’m in a hurry in the morning.

Russian uses the imperfective here because the sentence talks about an ongoing or repeated situation, not a single completed action.

• спешить = to hurry, to be in a hurry
• imperfective is normal for states, processes, and habits

A perfective verb would not fit this meaning well here. The sentence is about what happens in general whenever that situation occurs.

Yes, but it is the habitual present.

Я беру here means something like:

• I take
• I still take
• I make a point of taking

So the sentence is not about one specific morning. It describes a usual pattern.

If you wanted a single future event, Russian would normally change both tense and aspect, for example:

Даже если я буду очень спешить утром, я всё равно возьму с собой банан или грушу.
= Even if I’m in a big hurry tomorrow morning / that morning, I’ll still take a banana or a pear with me.

С собой means with oneself / along with oneself.

The expression брать с собой is very common and means:

• to take something with you
• to bring something along

So:

• беру банан = I take/pick up a banana
• беру с собой банан = I take a banana with me

Without с собой, the idea of bringing it along is weaker or may be missing.

Because с собой uses the instrumental case.

The pronoun is себя in its basic dictionary form, but it changes by case:

• nominative: no nominative form for себя
• genitive: себя
• dative: себе
• accusative: себя
• instrumental: собой
• prepositional: себе

After с in this fixed expression, Russian uses собой:

• брать с собой
• носить с собой
• взять с собой

Because Russian often uses the instrumental case to express time words like in the morning, during the day, in the evening, etc.

So:

• утром = in the morning
• днём = during the day
• вечером = in the evening
• ночью = at night

This is a very common pattern, and no preposition is needed.

Both words are direct objects, so they are in the accusative case.

But the accusative looks different depending on gender and animacy.

• банан is masculine inanimate, and for masculine inanimate nouns, the accusative usually looks the same as the nominative:

  • nominative: банан
  • accusative: банан

• груша is feminine, and feminine nouns in -а usually change to -у in the accusative:

  • nominative: груша
  • accusative: грушу

So беру банан или грушу is exactly what we expect.

Russian often repeats the subject in each clause, especially when the clauses are clearly separate.

So this is very natural:

Даже если я очень спешу утром, я всё равно беру...

You can sometimes omit the second я if the subject is obvious, but repeating it sounds clearer and more standard here.

Because Даже если я очень спешу утром is a subordinate clause introduced by если.

Russian normally separates a subordinate clause from the main clause with a comma:

Даже если я очень спешу утром, я всё равно беру с собой...

This is standard punctuation.

Yes. Russian word order is flexible.

This version is natural and emphasizes the concessive idea first:

Даже если я очень спешу утром, я всё равно беру с собой банан или грушу.

Other possible arrangements are:

• Утром, даже если я очень спешу, я всё равно беру с собой банан или грушу.
• Я всё равно беру с собой банан или грушу, даже если утром очень спешу.

The basic meaning stays similar, but the emphasis shifts slightly.

In careful writing, yes: всё равно.

In everyday Russian, many people write все равно, leaving out the dots over ё. Native speakers usually understand it from context, but for learners it is better to write ё when possible.

Here it is definitely pronounced всё, not все.

Yes, very often.

Both are natural:

• я спешу = I’m hurrying / I’m in a hurry
• я тороплюсь = I’m hurrying / I’m rushing

In many contexts they are very close in meaning. So this would also sound good:

Даже если я очень тороплюсь утром, я всё равно беру с собой банан или грушу.

The sentence you were given is perfectly normal; тороплюсь is just a common alternative.