Learn Russian: Кто-нибудь мыл сегодня эти грязные ступеньки? - Did someone wash these dirty steps today?

Кто-то means "someone" (you know a person did it, you just don't know who), while кто-нибудь means "anyone" (you don't even know if the event happened). Because this is a genuine question asking whether the action took place at all, кто-нибудь is the right choice.

Why is the imperfective verb мыл used here instead of a perfective verb like помыл or вымыл?

The speaker is asking about the general fact of an action—whether the event of washing happened at all today. In Russian, asking "did this take place?" often triggers the imperfective aspect. If they used a perfective verb, it would focus heavily on the successful completion and result, but мыл simply asks if the process happened.

What case is эти грязные ступеньки in this sentence?

It is in the accusative case because it's the direct object of the verb мыл. Since ступеньки (steps) is an inanimate noun, its plural accusative form looks exactly the same as its nominative (dictionary) form.

What is the singular form of ступеньки, and how is it different from лестница?

The singular is ступенька (a step or stair). While лестница refers to an entire staircase or ladder as a whole, ступеньки refers to the individual steps you walk on.