Neben dem Fenster steht ein bequemer Sessel, und dahinter brennt eine Kerze.

and

Breakdown of Neben dem Fenster steht ein bequemer Sessel, und dahinter brennt eine Kerze.

• dem: the; (masculine or neuter, dative)
• stehen: to stand
• das Fenster: the window

Questions & Answers about Neben dem Fenster steht ein bequemer Sessel, und dahinter brennt eine Kerze.

What case is dem Fenster in, and why is it dative here?

dem Fenster is in the dative case. The preposition neben can take either dative or accusative, depending on whether it expresses location (dative) or direction/movement (accusative). Here we’re talking about the location “next to the window,” so neben governs the dative.

Why does the sentence start with Neben dem Fenster, and how does that affect word order?

German is a V2 (verb-second) language. When you front a prepositional phrase (Neben dem Fenster) for emphasis or style, the finite verb (steht) must occupy the second position. The subject (ein bequemer Sessel) follows the verb. In English we’d say “Next to the window a comfortable armchair stands,” but we’d normally invert that.

Why is there a comma before und in … Sessel, und dahinter …? I thought commas before “and” in German were optional.

Correct, commas before coordinating conjunctions like und are generally optional in German. However, a comma is often used to clarify when each clause has its own subject and verb. Here you have two independent clauses:
1) … steht ein Sessel
2) … brennt eine Kerze
Putting a comma before und makes that division clearer, though you could omit it in everyday writing.

Why does bequemer end in -er? I expected something like bequeme or .