Den Fleck auf dem Tisch wische ich sofort mit der Küchenrolle ab.

German often moves one element to the front of the sentence to make it the topic or to give it extra focus.

So:

• Ich wische den Fleck ... ab. = neutral
• Den Fleck ... wische ich ... ab. = the stain is put in the spotlight

This kind of fronting is very common in German. Even when something other than the subject comes first, the finite verb still has to stay in second position, which is why you get:

• Den Fleck
  • wische
    • ich ...

Because Fleck is the direct object here, and masculine nouns in the singular take den in the accusative.

• nominative: der Fleck
• accusative: den Fleck

The verb abwischen takes a direct object, so the thing being wiped is in the accusative.

Because auf is a two-way preposition:

• dative for location (where?)
• accusative for direction/movement toward a place (where to?)

Here the stain is already located on the table, so this is location, not movement:

• auf dem Tisch = on the table

Compare:

• Der Fleck ist auf dem Tisch. = location
• Ich lege das Buch auf den Tisch. = movement onto the table

It is best understood as a phrase that modifies den Fleck by specifying which stain we mean: the one on the table.

So the object is still den Fleck, but auf dem Tisch is attached to it as extra information.

You can think of it like this:

• den Fleck [auf dem Tisch]

In English, this works similarly in the stain on the table.

Because mit always takes the dative.

So:

• die Küchenrolle = nominative
• mit der Küchenrolle = dative after mit

This is not because of the verb; it is simply the rule of the preposition mit.

Because abwischen is a separable verb.

Its parts are:

• ab- = prefix
• wischen = verb stem

In a normal main clause, the verb splits:

• Ich wische den Fleck ab.

So in your sentence:

• Den Fleck auf dem Tisch wische ich sofort mit der Küchenrolle ab.

The conjugated part wische goes to the usual verb position, and the prefix ab goes to the end.

When the verb is not split, the parts stay together:

• infinitive: abwischen
• subordinate clause: ..., weil ich den Fleck sofort mit der Küchenrolle abwische.

So:

• main clause: Ich wische den Fleck ab.
• subordinate clause: ..., weil ich den Fleck abwische.

This is a very common pattern with separable verbs.

Because German main clauses follow the verb-second rule.

If the first position is taken by something other than the subject, then the subject usually comes after the finite verb.

So here:

1. Den Fleck auf dem Tisch = first position
2. wische = second position
3. ich = subject comes after the verb

This is normal German word order, not an inversion for a question.

Yes, sofort can move around somewhat, because German adverbs are fairly flexible.

Here it appears in a natural middle position:

• Den Fleck auf dem Tisch wische ich sofort mit der Küchenrolle ab.

You could also hear:

• Ich wische den Fleck sofort mit der Küchenrolle ab.
• Ich wische sofort den Fleck mit der Küchenrolle ab.
• Sofort wische ich den Fleck mit der Küchenrolle ab.

These versions are all possible, but the emphasis changes slightly. The sentence you were given sounds natural and idiomatic.

Yes. That is a completely normal, more neutral version.

Compare:

• Ich wische den Fleck auf dem Tisch sofort mit der Küchenrolle ab.
  More neutral statement.

• Den Fleck auf dem Tisch wische ich sofort mit der Küchenrolle ab.
  More emphasis on the stain on the table.

Both are grammatically correct.

A useful breakdown is:

• Den Fleck auf dem Tisch = accusative object, fronted for emphasis
• wische = finite verb
• ich = subject
• sofort = adverb
• mit der Küchenrolle = prepositional phrase
• ab = separable prefix

So the underlying neutral version is roughly:

• Ich wische den Fleck auf dem Tisch sofort mit der Küchenrolle ab.

The sentence you have simply moves the object phrase to the front.