Сегодня я снова положила косметичку в сумку, чтобы не забыть тушь и помаду дома.

Yes, Russian can often omit subject pronouns, but here я is very useful.

In the past tense, the verb does not show person. Положила only tells you that the subject is feminine singular. By itself, it could mean I put, you put, or she put, depending on context.

So я makes the subject explicit: I.

You could omit it if the context already makes it obvious:

Сегодня снова положила косметичку в сумку...

That would still be grammatical, but less explicit.

Russian past tense agrees with the subject in gender and number.

• положил = masculine singular
• положила = feminine singular
• положило = neuter singular
• положили = plural

So я положила tells you that the speaker is female.

If a male speaker said the same sentence, it would be:

Сегодня я снова положил косметичку в сумку...

Because косметичку is the accusative singular form.

The noun косметичка is the direct object of положила: it is the thing being put somewhere.

For most feminine nouns ending in -а, the accusative singular changes to -у:

• косметичка → косметичку
• сумка → сумку
• помада → помаду

So:

• косметичка = nominative, dictionary form
• косметичку = accusative, used as the object

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

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

Here the idea is put into the bag, so Russian uses the accusative:

• в сумку = into the bag

Compare:

• Я положила косметичку в сумку. = I put the makeup bag into the handbag.
• Косметичка лежит в сумке. = The makeup bag is in the handbag.

So в сумку is used because the sentence describes movement to a destination.

This is a question of aspect.

Russian has two main aspects:

• imperfective: process, repetition, ongoing action
• perfective: completed single action, result

Here the speaker means a completed action: she put the bag in there, and the action is done. So Russian uses the perfective verb положить:

• положила = put, placed, completed the act

The imperfective partner is класть:

• клала would suggest something like a repeated action, a process, or a descriptive background action

So in this sentence, положила is the natural choice because it focuses on the completed result.

Чтобы introduces a clause of purpose. It often means:

• so that
• in order to
• so as to

So:

чтобы не забыть тушь и помаду дома
= so as not to forget the mascara and lipstick at home

A very important point: when the subject is the same as in the main clause, Russian often uses чтобы + infinitive.

Here the subject is the same person in both parts:

• я положила
• so that I would not forget

That is why Russian uses the infinitive забыть.

If the subject were different, Russian would usually use a finite verb instead:

• Я положила косметичку в сумку, чтобы муж не забыл тушь.

Also, не simply negates the infinitive:

• не забыть = not to forget

Again, this is about aspect.

• забывать = imperfective, forgetting in general or as a repeated habit
• забыть = perfective, to forget on a specific occasion

Here the speaker means avoiding one specific mistake: leaving those items at home this time. So the perfective infinitive забыть is natural.

The idea is not so that I would not be in the habit of forgetting, but rather so that I do not forget them this time.

Both words are direct objects, so both are in the accusative. But they belong to different noun patterns.

тушь

This is a feminine noun ending in a soft sign, a third-declension noun. In the singular, its nominative and accusative forms are the same:

• тушь = nominative
• тушь = accusative

помада

This is a feminine noun ending in -а, so its accusative singular changes:

• помада → помаду

So the difference is not about meaning. It is just how the two noun types decline.

Because дома here is an adverb meaning at home.

Russian often uses дома without any preposition in expressions like:

• быть дома = to be at home
• оставить дома = to leave at home
• забыть дома = to forget at home

So:

не забыть тушь и помаду дома
means
not to forget the mascara and lipstick at home

In other words, not to leave them behind at home.

This is a very common Russian pattern.

Снова means again.

Yes, опять could also mean again, and in many contexts the two are close:

• снова = again
• опять = again

But there is a small nuance:

• снова often sounds a bit more neutral or slightly more formal/bookish
• опять can sometimes sound more emotional, especially if the speaker is annoyed: again?!

In this sentence, снова sounds natural and neutral.

No. Russian word order is fairly flexible, because case endings show the grammatical roles.

The version given is a natural neutral sentence:

Сегодня я снова положила косметичку в сумку, чтобы не забыть тушь и помаду дома.

But other word orders are possible, with different emphasis:

• Я сегодня снова положила косметичку в сумку...
• Косметичку я сегодня снова положила в сумку...
• Чтобы не забыть тушь и помаду дома, я сегодня снова положила косметичку в сумку.

The meaning stays basically the same, but the focus shifts.

For example, putting сегодня first makes today the starting point of the sentence, while putting косметичку first gives extra emphasis to the makeup bag.