Wir decken den Teller mit Alufolie ab, damit das Essen warm bleibt.

Because the verb is abdecken, which is a separable verb.

• Infinitive: abdecken = to cover
• In a normal main clause, the verb splits:
  • Wir decken den Teller mit Alufolie ab.

So:

• decken goes to the usual verb position
• ab moves to the end

This is very common in German:

• Ich mache das Fenster auf. = I open the window.
• Sie räumt das Zimmer auf. = She tidies up the room.

If the verb stays in the infinitive or another non-finite form, it does not split:

• Wir wollen den Teller mit Alufolie abdecken.

On its own, decken often does mean to set or to cover, depending on context. But here the full verb is abdecken, and that specifically means to cover up.

So in this sentence:

• den Teller abdecken = to cover the plate/dish

This is different from:

• den Tisch decken = to set the table

So it is important to learn abdecken as its own verb, not just decken + ab in a literal English-style way.

Because der Teller is masculine, and here it is the direct object of the verb abdecken.

The cases are:

• Nominative: der Teller
• Accusative: den Teller

In the sentence:

• Wir = subject
• decken = verb
• den Teller = direct object

So German uses the accusative:

• Wir decken den Teller ab.

The preposition mit always takes the dative case.

Here, Alufolie means aluminum foil / tin foil and is a feminine noun:

• nominative: die Alufolie
• dative: der Alufolie

So if you include the article, you would say:

• mit der Alufolie

But German often leaves out the article with materials or substances when speaking generally, so:

• mit Alufolie = with aluminum foil

That sounds natural here.

Damit means so that or in order that. It introduces a purpose clause.

So:

• Wir decken den Teller mit Alufolie ab, damit das Essen warm bleibt.
• We cover the plate with aluminum foil so that the food stays warm.

It explains why we are doing the action.

A useful comparison:

• um ... zu = in order to, when the subject is the same
• damit = so that, often when there is a full clause with its own verb

Here the clause has its own subject, das Essen, so damit is the natural choice.

Because damit introduces a subordinate clause, and in German subordinate clauses send the finite verb to the end.

Main clause:

• Wir decken den Teller mit Alufolie ab.

Subordinate clause:

• damit das Essen warm bleibt

That final position of bleibt is completely normal after words like:

• weil = because
• dass = that
• wenn = if/when
• damit = so that

For example:

• Ich bleibe zu Hause, weil ich krank bin.
• Sie kommt früher, damit wir anfangen können.

Bleiben means to remain / stay, so warm bleibt means stays warm.

That fits the idea of preserving a state:

• The food is already warm.
• Covering it helps it remain warm.

If you said warm ist, that would just mean is warm, which does not express the idea of continuing to be warm.

So:

• warm ist = is warm
• warm bleibt = stays warm / remains warm

Because warm here is a predicate adjective, not an adjective directly before a noun.

Compare:

• das warme Essen = the warm food
  
  • adjective before a noun, so it takes an ending
• das Essen bleibt warm = the food stays warm
  
  • predicate adjective, so no ending

After verbs like:

• sein = to be
• werden = to become
• bleiben = to stay

adjectives usually stay in their basic form:

• Das Haus ist groß.
• Sie wird müde.
• Das Essen bleibt warm.

Das Essen is the subject of the subordinate clause:

• damit das Essen warm bleibt

So inside that clause:

• das Essen = subject
• bleibt = verb
• warm = predicate adjective

Even though the whole sentence starts with Wir, the subordinate clause has its own subject.

English does the same thing:

• We cover the plate ... so that the food stays warm.

Yes, Teller literally means plate, and the sentence is still natural enough. In everyday German, people often describe the physical object being covered, even when the real purpose is to protect or insulate the food on it.

So:

• den Teller mit Alufolie abdecken = cover the plate with foil

Depending on context, a speaker might also say:

• das Essen mit Alufolie abdecken = cover the food with foil
• die Schüssel mit Alufolie abdecken = cover the bowl with foil

All of these are possible; the sentence you have is simply focusing on the plate as the thing being covered.

German present tense often covers both the English simple present and present progressive, depending on context.

So:

• Wir decken den Teller mit Alufolie ab can mean:
  • We cover the plate with aluminum foil
  • We are covering the plate with aluminum foil

German usually does not need a special form like English are covering. The situation tells you which meaning is intended.

Not naturally in this exact structure, because um ... zu is usually used when the subject of both actions is the same and when you can express the purpose without a new finite clause.

Here the purpose clause is:

• damit das Essen warm bleibt

Its subject is das Essen, not wir, so damit works better.

A version with um ... zu would need a different structure, for example:

• Wir decken den Teller mit Alufolie ab, um das Essen warm zu halten.
• We cover the plate with aluminum foil in order to keep the food warm.

That is also correct, but it changes the wording:

• damit das Essen warm bleibt = so that the food stays warm
• um das Essen warm zu halten = in order to keep the food warm