Das schwerste Möbelstück tragen wir zu zweit, obwohl die Spedition helfen will.

Because Möbelstück is neuter (das Möbelstück) and the adjective is in the nominative neuter singular with the definite article (das). With definite articles, adjectives take the “weak” ending, so you get das schwerste Möbelstück.

• das schwerste Möbelstück = the heaviest piece of furniture

The base adjective is schwer (heavy). The attributive superlative is usually formed with -st- plus adjective endings:

• schwer → schwerst- → schwerste (because it’s followed by a noun and needs an ending)
  Compare:
• Predicative: Das Möbelstück ist am schwersten.
• Attributive: das schwerste Möbelstück

Möbel is a collective noun meaning “furniture” (often treated like plural-only in everyday use). Möbelstück means “piece of furniture,” which is countable and can be compared easily:

• das Möbelstück = the piece of furniture
• das schwerste Möbelstück = the heaviest piece of furniture

German main clauses follow the V2 rule: the finite verb (here tragen) is in the second position. The first position can be occupied by many things (not necessarily the subject). Here the object is placed first for emphasis/topic:

• Das schwerste Möbelstück (position 1)
• tragen (position 2)
• wir (subject comes after the verb)

Yes. That’s the neutral word order with the subject first. The given sentence front-loads das schwerste Möbelstück to highlight it (topic/emphasis), but both are correct.

zu zweit is an idiomatic adverbial phrase meaning “as a pair / the two of us / two people together.”
You can also get:

• zu dritt = three people together
• zu viert = four people together
  It’s a fixed expression; you generally don’t translate the zu literally.

Context plus grammar. The subject is wir, so zu zweit naturally describes how we carry it: “we carry it, the two of us.” If you wanted to be explicit, you could add something like wir beide (we both), but it’s often unnecessary.

obwohl introduces a subordinate clause, and in subordinate clauses the finite verb goes to the end (verb-final order):

• ..., obwohl die Spedition helfen will.
  Here will is the finite verb, so it comes last; helfen is an infinitive placed right before it.

Both express contrast (“although / nevertheless”), but the grammar differs:

• obwohl starts a subordinate clause: ..., obwohl die Spedition helfen will.
• trotzdem is an adverb in a main clause and follows V2 rules: Die Spedition will helfen; trotzdem tragen wir es zu zweit.

In subordinate clauses, the finite verb (will) goes to the end, and the infinitive (helfen) stays directly before it. In a main clause you’d say:

• Die Spedition will helfen. (V2: will in second position)

die Spedition refers to a shipping company / moving company / freight forwarding company—basically the professional company handling transport. In a moving context, it’s the movers.

It’s simply the grammatical gender of the noun: die Spedition. Many nouns ending in -ion are feminine in German (e.g., die Situation, die Information), and Spedition follows that pattern.

helfen normally takes a dative object (help someone):

• Die Spedition will uns helfen.
  In your sentence, the object (uns) is understood from context and can be omitted because it’s obvious who would be helped.

No—zu zweit explicitly means two people together, not alone. The contrast is: “We carry it as two people, although the moving company wants to help (too).” If it were “alone,” you’d use allein or zu zweit ohne Hilfe would be contradictory.

It expresses concession (a “despite the fact that…” idea), not a reason. The meaning is: even though help is offered, we still do it as two people.

German requires a comma before subordinate clauses introduced by conjunctions like obwohl, weil, dass, etc. So the comma before obwohl is mandatory in standard writing.

Not in the same way. schwerste here is singular and attached to a singular noun. If you used a plural noun, you’d need plural agreement:

• die schwersten Möbelstücke = the heaviest pieces of furniture
  Using Möbel is trickier because it’s collective; you’d more naturally say das schwerste Möbelstück when comparing items.