Я положила спички в рюкзак рядом с горелкой и маленьким котелком.

Because положила is the past tense feminine singular form of the verb.

In Russian past tense, the verb agrees with the subject in gender and number:

• я положил = I put (said by a male speaker)
• я положила = I put (said by a female speaker)
• мы положили = we put

So this sentence tells you that the speaker is female.

Положила comes from положить, which is a perfective verb.

Perfective verbs usually present an action as a single completed whole. Here, the idea is that the speaker finished putting the matches into the backpack.

A common aspect pair is:

• класть = imperfective, to put / be putting / put repeatedly
• положить = perfective, to put once, successfully, completely

So:

• Я клала спички... = I was putting / used to put matches...
• Я положила спички... = I put the matches... / I have put the matches...

Also, learners often notice ложить. In standard Russian, the normal imperfective partner of положить is класть, not ложить.

It has changed grammatically, but for this noun the accusative plural looks the same as the nominative plural.

• nominative plural: спички
• accusative plural: спички

This happens because спички is an inanimate plural noun, and for many inanimate nouns, nominative and accusative are identical.

So in this sentence, спички is the direct object of положила.

It does have a singular form:

• singular: спичка = a match
• plural: спички = matches

In this sentence, plural is used because the speaker put more than one match.

Because Russian uses different cases depending on whether you mean movement into something or location inside something.

With в:

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

So:

• в рюкзак = into the backpack
• в рюкзаке = in the backpack

Since the action is putting something into the backpack, Russian uses accusative: в рюкзак.

Because рядом с requires the instrumental case.

So after рядом с (next to / beside), the nouns must be in instrumental:

• горелка → с горелкой
• котелок → с котелком

This is just a fixed grammar pattern:

• рядом с другом = next to a friend
• рядом с домом = next to the house
• рядом с горелкой = next to the burner

Because the two nouns have different genders and declension patterns, even though both are in the instrumental singular.

• горелка is feminine → instrumental singular: горелкой
• котелок is masculine → instrumental singular: котелком

So the different endings are normal and expected.

Маленьким is the adjective маленький (small) in the instrumental singular masculine form, because it agrees with котелком.

Agreement in Russian means the adjective matches the noun in:

• gender
• number
• case

So:

• маленький котелок = a small pot
• с маленьким котелком = next to a small pot

Here it is instrumental because of рядом с.

In this sentence, маленьким most naturally describes only котелком.

So the phrase means:

• next to the burner
• and the small pot

If the speaker wanted to say that both were small, Russian would usually make that clearer, for example by repeating the adjective:

• рядом с маленькой горелкой и маленьким котелком

As written, the adjective is attached only to the second noun.

It means the matches were put into the backpack, and inside it they were placed next to the burner and the small pot.

The structure is:

• положила спички в рюкзак = put the matches into the backpack
• рядом с горелкой и маленьким котелком = next to the burner and small pot

So the burner and pot are understood as the nearby items inside the backpack.

If you wanted to say next to the backpack, you would say something like:

• Я положила спички рядом с рюкзаком.

Sometimes yes, but here Я is very helpful.

In Russian, subject pronouns are often omitted when the meaning is clear from context. But in the past tense, the verb does not show person clearly:

• положила could mean I put or she put, depending on context

So Я removes that ambiguity.

That is why Я положила... sounds natural and clear.

No, Russian word order is fairly flexible. The sentence as given has a neutral, natural order.

• Я положила спички в рюкзак рядом с горелкой и маленьким котелком.

But you could rearrange parts to emphasize something different:

• Спички я положила в рюкзак... = emphasizes matches
• В рюкзак я положила спички... = emphasizes into the backpack
• Я спички положила в рюкзак... = possible in speech, with a different emphasis

So the original order is not the only possible one; it is just the most straightforward.

Russian has no articles like English a and the.

So:

• в рюкзак can mean into a backpack or into the backpack
• с горелкой can mean with / next to a burner or the burner

Context tells you which one is meant.

That is very normal in Russian, and learners have to get used to understanding definiteness from the situation rather than from articles.