После ужина я выброшу пустую бутылку.

Because после requires the genitive case.

• ужин = dinner
• genitive singular of ужин = ужина

So:

• после ужина = after dinner

This is something you simply have to learn with the preposition: после + genitive.

Выброшу is the 1st person singular future of the perfective verb выбросить.

Russian has two common ways to talk about the future:

1. Perfective verb → simple future

   • я выброшу = I will throw away / I’ll throw out

2. Imperfective verb → буду + infinitive

   • я буду выбрасывать = I will be throwing away / I will throw away repeatedly or in process

Here, выброшу is used because the speaker means one completed action: after dinner, I will throw the empty bottle away.

The prefix вы- adds the idea of out or away.

• бросить = to throw
• выбросить = to throw out, throw away

So in this sentence, the meaning is not just throw, but specifically get rid of by throwing away.

This is a normal stem change in Russian conjugation.

• infinitive: выбросить
• я form: выброшу

The с changes to ш before the ending. This happens in a number of verbs, for example:

• просить → я прошу
• носить → я ношу

So выброшу is not irregular in a random way; it follows a common pattern.

Also remember: since выбросить is perfective, forms like выброшу are future, not present.

Because бутылку is the direct object, so it is in the accusative case.

• nominative: бутылка
• accusative singular: бутылку

The verb выброшу is acting on the bottle, so the bottle is the thing being thrown away.

So:

• я выброшу бутылку = I will throw away the bottle

The adjective has to agree with the noun in gender, number, and case.

Here:

• бутылка is feminine singular
• in the sentence it is accusative singular
• so пустая changes to пустую

Comparison:

• nominative: пустая бутылка = an empty bottle
• accusative: пустую бутылку = an empty bottle as the object of the verb

So both words change together:

• пустая бутылка
• пустую бутылку

Russian has no articles.

So бутылку can mean:

• a bottle
• the bottle

The exact meaning comes from context.

In this sentence, English might translate it as either:

• After dinner I’ll throw away an empty bottle
• After dinner I’ll throw away the empty bottle

Both are possible depending on the situation.

Yes, often you can.

Russian frequently drops subject pronouns when the verb ending already makes the subject clear.

• После ужина выброшу пустую бутылку.
• После ужина я выброшу пустую бутылку.

Both are natural.

Including я can make the subject a little more explicit, or add slight emphasis, especially if there is contrast:

• Я выброшу бутылку, а ты помоешь посуду.

Yes. Russian word order is flexible, although different orders change the emphasis.

This sentence:

• После ужина я выброшу пустую бутылку.

is very natural and puts the time phrase first: after dinner.

Other possible orders:

• Я выброшу пустую бутылку после ужина.
  More straightforward, with the time phrase at the end.

• Пустую бутылку я выброшу после ужина.
  Emphasizes the empty bottle.

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

Not necessarily.

После ужина simply means after dinner. It could mean right after, or just sometime later, depending on context.

If you want to make immediately after clearer, Russian often uses:

• сразу после ужина = right after dinner

So:

• После ужина я выброшу пустую бутылку. = After dinner I’ll throw away the empty bottle.
• Сразу после ужина я выброшу пустую бутылку. = Right after dinner I’ll throw away the empty bottle.

A natural stress pattern is:

По́сле у́жина я вы́брошу пусту́ю буты́лку.

Rough pronunciation guide:

• По́сле = POS-le
• у́жина = OO-zhi-na
• вы́брошу = VY-bra-shu / VY-bro-shu
• пусту́ю = poos-TOO-yu
• буты́лку = boo-TIL-ku

A few helpful notes:

• ж sounds like the s in measure
• ш sounds like sh
• unstressed vowels are often reduced in real speech, so pronunciation may sound less exact than the spelling suggests

It normally describes a single future action.

That is because выброшу comes from the perfective verb выбросить, which presents the action as completed.

So the sentence means something like:

• after dinner, I will throw the empty bottle away

If you wanted to describe a repeated habit, Russian would usually choose an imperfective form and probably a different context, for example:

• После ужина я обычно выбрасываю пустые бутылки.
  After dinner I usually throw away empty bottles.

So in your sentence, the default reading is one specific future event.