Learn Hardcore Turkish: Emlakçı, kiralık daire gösterecek.

No. In standard Turkish you do not place a comma between the subject and the verb. The natural version is: Emlakçı kiralık daire gösterecek. Use a comma only with appositions or long/parenthetical subjects (e.g., Emlakçı Ali Bey, yarın…).

Why doesn’t daire have the accusative ending -i?

Because the object is non-specific (indefinite). Turkish marks specific/definite direct objects with -(y)i.

Non-specific: Emlakçı kiralık daire gösterecek. = will show a rental apartment (some apartment).
Specific: Emlakçı kiralık daireyi gösterecek. = will show the rental apartment (a particular one we have in mind).

Does kiralık daire mean one apartment or more?

It’s number-neutral. Without -ler, Turkish often leaves number vague; in English it’s usually translated as singular. To force plural, say kiralık daireler gösterecek. To refer to a specific set, use the accusative plural: kiralık daireleri gösterecek.

Do I need bir to mean “a”? Should I say kiralık bir daire?

No, bir is optional. Without it, the object is already indefinite. Use kiralık bir daire to emphasize a single, countable apartment. Place bir before the noun, after the adjective: kiralık bir daire (not bir kiralık daire, which sounds like “one rental apartment” in the numeric sense or is stylistic).

What nuance does the future -ecek have? Could I use the present continuous instead?