Для похода мама взяла горелку, котелок и сухие дрова.

Because для always takes the genitive case in Russian.

• поход = nominative dictionary form
• похода = genitive singular

So для похода means for the hike / for the camping trip.

A useful contrast:

• для похода = for the trip
• в поход = on the trip / on a hike, especially after a verb of motion

So the form is not random; it is required by для.

In the past tense, Russian verbs agree with the subject in gender and number.

Here the subject is мама, which is feminine singular, so the verb must be взяла.

Past tense forms:

• masculine: взял
• feminine: взяла
• neuter: взяло
• plural: взяли

So:

• Мама взяла = Mom took
• Папа взял = Dad took

All three words are direct objects, so they are in the accusative case. But different kinds of nouns form the accusative differently.

1. горелка → горелку

This is a feminine noun ending in -а.
In the accusative singular, -а usually changes to -у.

• горелка → горелку

2. котелок → котелок

This is a masculine inanimate noun.
For masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

• котелок → котелок

3. дрова → дрова

This is an inanimate plural noun.
For inanimate plural nouns, the accusative is usually the same as the nominative plural.

• дрова → дрова

So all three are accusative, but they look different because they follow different declension patterns.

Because дрова is grammatically plural, and the adjective has to agree with it.

• сухие = plural form of сухой
• дрова = plural noun

So the adjective must also be plural:

• сухие дрова = dry firewood

You cannot use a singular adjective here, because the noun is not singular.

Yes, and this is a great example of how Russian and English divide things differently.

In Russian, дрова is a plural-only noun. It refers to firewood as a collection of pieces/logs, so it normally appears only in the plural.

That means Russian treats it more like logs than like the English mass noun firewood.

So:

• дрова = firewood / logs
• сухие дрова = dry firewood

This is normal Russian usage.

Поход usually means an outdoor trip such as a hike, trek, camping trip, or excursion, often involving gear, cooking, and spending time in nature.

So in this sentence, it sounds more like:

• a hiking trip
• a camping outing
• an outdoor excursion

It is usually more substantial than a simple walk.

For a casual walk, Russian would more likely use:

• прогулка = walk, stroll

So для похода suggests real outdoor preparation.

These are common outdoor/camping words.

• горелка = a burner, often a camping stove or gas burner
• котелок = a small camping pot, mess tin, or metal cooking pot used outdoors

So the sentence gives a very natural list of hiking/camping supplies.

This is about aspect, one of the most important parts of Russian verbs.

• взять = perfective
• брать = imperfective

Here the speaker is talking about a completed action: Mom took/packed these things for the trip. That is why взяла is used.

Very roughly:

• взяла = she took, she grabbed, she packed up
• брала = she was taking, used to take, was in the process of taking

In a sentence that simply lists what someone took once, the perfective взяла is the natural choice.

Yes. Russian word order is fairly flexible because cases show what each word is doing.

This sentence begins with Для похода, which puts the purpose first:

• Для похода мама взяла... = For the hike, Mom took...

You could also say:

• Мама взяла для похода горелку, котелок и сухие дрова.

That version is also correct. The difference is mostly one of emphasis and information flow, not core meaning.

Putting Для похода first slightly highlights the context or purpose.

Because Russian has no articles.

Russian does not have separate words corresponding to English a/an and the. So:

• мама can mean mom, a mother, or the mother, depending on context
• горелку can mean a burner or the burner

English requires articles; Russian usually leaves that information to context.

Because this is a simple list of three items:

• горелку
• котелок
• сухие дрова

In Russian, as in normal English list punctuation, you put commas between earlier items, but not before the final и in a simple list.

So:

• горелку, котелок и сухие дрова

is the standard punctuation.