Opróżnij butelkę tak dokładnie jak słoik.

It is the 2nd person singular imperative of opróżnić.

So it means empty! said to one person.

A useful extra point: opróżnić is perfective, so opróżnij suggests empty it completely / finish emptying it.

Compare:

• opróżnij = empty it out completely
• opróżniaj = be emptying it / empty it regularly / keep emptying it

Because butelka is the direct object of the verb opróżnić.

After this verb, the thing being emptied goes in the accusative case.

• nominative: butelka = bottle
• accusative: butelkę = bottle as the object

So:

• Butelka stoi na stole = The bottle is standing on the table.
• Opróżnij butelkę = Empty the bottle.

Because dokładnie is an adverb, and it describes how the action is done.

Here it modifies the verb:

• opróżnij ... dokładnie = empty ... thoroughly / carefully / completely

The adjective forms dokładny / dokładna / dokładne would describe a noun, not the action.

So:

• dokładny opis = an accurate description
• zrób to dokładnie = do it carefully / precisely

Yes. Dokładnie is a very flexible word.

Depending on context, it can mean:

• exactly
• precisely
• carefully
• thoroughly

In this sentence, because the verb is opróżnić (to empty), dokładnie means something like:

• thoroughly
• completely
• leaving nothing behind

So the sense is not exactly, but very completely / very thoroughly.

Tak ... jak is a common comparison pattern meaning as ... as.

In this sentence:

• tak dokładnie jak = as thoroughly as

So the structure is:

• tak
  • adverb/adjective + jak

Examples:

• tak szybko jak on = as fast as him / as he does
• tak dobrze jak ty = as well as you
• tak dokładnie jak słoik = as thoroughly as the jar

A close alternative is równie ... jak:

• równie dokładnie jak ... = equally as thoroughly as ...

Because słoik is jar, and here it is the thing used for comparison.

A detail that often confuses learners: słoik is a masculine inanimate noun, and in the singular, its accusative form is the same as its nominative form:

• nominative: słoik
• accusative: słoik

So even if you expect some kind of object form, słoik still looks the same.

That is normal for many masculine inanimate nouns in Polish.

It is understandable, but it feels a bit elliptical—that is, slightly shortened.

A fuller version would be something like:

• Opróżnij butelkę tak dokładnie, jak opróżniłeś słoik.
• Opróżnij butelkę tak dokładnie, jak opróżniono słoik.

In everyday speech, Polish often leaves out words that are understood from context. So the shorter sentence is possible, but without context it may sound a little unusual because you are comparing emptying a bottle to a jar, and the listener has to mentally supply the missing idea.

Because Polish usually omits subject pronouns when they are already clear from the verb form.

The form opróżnij already tells you that the command is addressed to you singular.

So:

• Opróżnij butelkę = Empty the bottle.
• Ty opróżnij butelkę = You empty the bottle.

The version with ty is possible, but it adds emphasis and is not the neutral default.

Usually no in the short version:

• Opróżnij butelkę tak dokładnie jak słoik.

That is treated like a short comparison.

But if you expand it into a full clause, then a comma is normally used:

• Opróżnij butelkę tak dokładnie, jak opróżniłeś słoik.

So a simple rule is:

• short comparison → usually no comma
• full clause after jak → comma

Use the plural imperative:

• Opróżnijcie butelkę tak dokładnie jak słoik.

So:

• opróżnij = empty it! said to one person
• opróżnijcie = empty it! said to more than one person

For polite singular/plural address, Polish also uses the plural-style form with pan / pani / państwo, but the simplest practical form to learn here is opróżnijcie for you all.