Bevor ich den Kuchen aus dem Backofen hole, brauche ich den Topflappen.

Because bevor introduces a subordinate clause. In German, the conjugated verb usually goes to the end of a subordinate clause.

So:

• Bevor ich den Kuchen aus dem Backofen hole
• literally follows the pattern Before I the cake out of the oven take

This is normal German word order after conjunctions like:

• bevor = before
• weil = because
• dass = that
• wenn = if/when

Because the whole bevor-clause comes first, and that counts as the first position in the sentence. In a German main clause, the conjugated verb must be in second position.

So the structure is:

• Bevor ich den Kuchen aus dem Backofen hole, = first position
• brauche = second position, so it must come next
• ich = after the verb

That is why you get:

• Bevor ..., brauche ich ...

and not:

• Bevor ..., ich brauche ...

Both are direct objects, so they are in the accusative case.

Also, both nouns are masculine singular:

• der Kuchen → den Kuchen in the accusative
• der Topflappen → den Topflappen in the accusative

So den here tells you:

• masculine
• singular
• accusative

Because the preposition aus always takes the dative case.

• der Backofen = nominative
• dem Backofen = dative

So:

• aus dem Backofen = out of the oven

This is just something to memorize with aus:

• aus + dative

For example:

• aus dem Haus
• aus der Küche
• aus dem Auto

Not in this sentence. Here, the main verb is simply holen, and aus dem Backofen is a prepositional phrase telling you where the cake is being taken from.

So the structure is:

• den Kuchen = object
• aus dem Backofen = from the oven
• holen = to get / take

German speakers could also say something like herausholen or rausholen in some contexts, but den Kuchen aus dem Backofen holen is completely natural and correct.

Because a subordinate clause and a main clause are being separated.

In German, clauses introduced by words like bevor, weil, dass, wenn, and similar conjunctions are normally set off with a comma.

So:

• Bevor ich den Kuchen aus dem Backofen hole, brauche ich den Topflappen.

The comma is required.

Because German often uses the present tense for the future when the meaning is clear from context.

Here, the idea is something like:

• first I will need the oven mitt
• then I will take the cake out

German does not need a future form here. The present tense sounds natural.

So brauche and hole can refer to a near-future action just fine.

Bevor is a conjunction that introduces a clause.

• Bevor ich den Kuchen aus dem Backofen hole ...
• Before I take the cake out of the oven ...

Vor is a preposition used with a noun phrase, not a full clause.

For example:

• vor dem Essen = before the meal
• vor dem Backofen = in front of the oven

So:

• bevor
  • clause
• vor
  • noun phrase

Yes. Ofen is shorter and very common in everyday speech, while Backofen is a bit more specific.

So both can work:

• aus dem Ofen
• aus dem Backofen

In many situations, Ofen would sound very natural. Backofen is useful when you want to be especially clear that you mean an oven for baking, not some other kind of stove or heater.

Grammatically, the sentence is talking about one oven mitt or potholder:

• der Topflappen = the potholder / oven mitt
• den Topflappen = accusative singular

German often uses the singular if one item is enough for the situation. If you wanted to say the oven mitts in the plural, it would be:

• die Topflappen

So the sentence would change to:

• ..., brauche ich die Topflappen.

But the original singular is completely normal.