Bevor die Kinder wiederkommen, wische ich die Krümel weg und lege den Topflappen neben den Herd.

Because bevor is a subordinating conjunction meaning before. In German, a clause introduced by a subordinating conjunction sends the conjugated verb to the end of that clause.

So:

• die Kinder kommen wieder = the children come back
• bevor die Kinder wiederkommen = before the children come back

Here, wiederkommen is the full verb, and in the subordinate clause it appears at the end.

Because the sentence begins with the subordinate clause Bevor die Kinder wiederkommen. That whole clause takes the first position in the sentence. In German main clauses, the conjugated verb must come second.

So the structure is:

• [Bevor die Kinder wiederkommen] [wische] [ich] ...

This is a very common pattern:

• Wenn ich Zeit habe, gehe ich spazieren.
• Bevor die Kinder wiederkommen, wische ich die Krümel weg.

So wische ich is required by normal German word order here.

Yes, wiederkommen is usually treated as a separable verb in this meaning: to come back / return.

In a normal main clause, it separates:

• Die Kinder kommen wieder. = The children come back.

But in a subordinate clause, separable verbs usually rejoin and appear as one word at the end:

• ..., bevor die Kinder wiederkommen.

So:

• main clause: kommen ... wieder
• subordinate clause: wiederkommen

Yes. wegwischen is a separable verb meaning something like to wipe away.

In a main clause, it separates:

• Ich wische die Krümel weg.

In a subordinate clause, it would be joined:

• ..., weil ich die Krümel wegwische.

This is the same basic pattern as with many separable verbs in German.

Krümel means crumbs. Here it is:

• plural
• accusative case
• the direct object of wische ... weg

The article die can mean several things in German, but here it is plural nominative/accusative. Since the crumbs are what gets wiped away, this is accusative plural.

Singular would be:

• der Krümel = the crumb

Plural:

• die Krümel = the crumbs

Because the same subject, ich, applies to both verbs:

• wische ich die Krümel weg
• und lege den Topflappen neben den Herd

German often leaves out the repeated subject when it is clearly the same in coordinated clauses.

So this is equivalent to:

• ..., wische ich die Krümel weg und ich lege den Topflappen neben den Herd.

But repeating ich would usually sound unnecessary here.

Because Topflappen is a masculine noun: der Topflappen.

In this sentence, it is the direct object of lege, so it takes the accusative case:

• nominative: der Topflappen
• accusative: den Topflappen

So:

• Ich lege den Topflappen ... = I put the oven mitt / pot holder ...

Because neben is a two-way preposition. It can take:

• dative for location: where something is
• accusative for direction/movement: where something is being put

Here, the verb legen implies movement to a new position: the speaker is placing the oven mitt next to the stove. So German uses the accusative:

• neben den Herd = to next to the stove

Compare:

• Der Topflappen liegt neben dem Herd. = The oven mitt is next to the stove.
  
  • location, so dative
• Ich lege den Topflappen neben den Herd. = I put the oven mitt next to the stove.
  
  • movement, so accusative

This is a very common German pair:

• legen = to lay / put something somewhere
  
  • usually takes a direct object
  • shows movement or placement
• liegen = to lie / be lying somewhere
  
  • no direct object in this meaning
  • shows location or state

So here:

• Ich lege den Topflappen neben den Herd. = I put the oven mitt next to the stove.
• Der Topflappen liegt neben dem Herd. = The oven mitt is lying next to the stove.

English often uses put and is instead, but German makes a clear distinction.

Because German uses a comma to separate a subordinate clause from the main clause.

So in:

• Bevor die Kinder wiederkommen, wische ich ...

the comma marks the end of the bevor clause.

This comma is required in standard German punctuation.

Der Herd usually means stove or cooker/range as the kitchen appliance in general. In many contexts, it refers to the cooking unit as a whole, not just the burners.

So depending on context, English translations might vary a little:

• stove
• cooker
• sometimes range

But in this sentence, next to the stove is a natural translation.

Yes, often you could. Both can mean come back / return, but they are not always identical in tone or usage.

• wiederkommen = come back, come again
• zurückkommen = return, come back to a previous place

In many everyday contexts, both work:

• Bevor die Kinder wiederkommen ...
• Bevor die Kinder zurückkommen ...

But wiederkommen is very natural in everyday speech here.