Mientras la plomera estaba trabajando, yo estaba limpiando el piso con un trapo.

Because the sentence describes two ongoing background actions happening at the same time. In Spanish, simultaneous ongoing actions in the past are typically expressed with the imperfect:

• Mientras la plomera estaba trabajando, yo estaba limpiando... = both actions were in progress. If you used the preterite, it would sound more like completed events (or would shift the focus to the start/end).

Both can be correct, but they emphasize slightly different things:

• Trabajaba (imperfect) = she worked / she was working (simple description of an ongoing past action).
• Estaba trabajando = she was in the middle of working (more vivid “in progress” feel). In many everyday contexts they’re interchangeable, but estar + gerundio often highlights the action as actively happening at that moment.

Mientras means while. It very often pairs with the imperfect when describing overlapping actions in the past.
It doesn’t always require the imperfect, but:

• Mientras + imperfect is the most common for “while something was happening…”
• If you use preterite, it usually marks a completed event or a change in the timeline (less “background,” more “event”).

No. Spanish often omits subject pronouns because the verb already shows the subject:

• ...estaba limpiando el piso... already implies I. You include yo for emphasis, contrast, or clarity:
• ...la plomera estaba trabajando, y yo estaba limpiando... (emphasizing that I, not someone else, was cleaning)

Yes. Plomero/plomera is common in Latin America for plumber.

• el plomero = male plumber
• la plomera = female plumber
  Using the feminine form is normal when the plumber is a woman.

Because they refer to different things:

• la plomera = a specific plumber known in the context (the plumber who came)
• un trapo = a rag (not necessarily a specific one; just one you used)

Con un trapo means with a rag / using a rag.
In most cases, Spanish prefers an article:

• con un trapo (natural) You might hear con trapo in some contexts, but it’s less standard and can sound incomplete unless it’s part of a set phrase or very casual speech.

Trapo is very common for rag/cloth in Latin America. Depending on the region, you might also hear:

• un paño = a cloth (often a bit “nicer” or more neutral than trapo)
• una franela (some countries) = cloth/flannel used for cleaning
  Trapo can sometimes imply an old cloth used for cleaning.

Spanish often uses the definite article with common household surfaces:

• limpiar el piso = clean the floor Dropping the article (limpiar piso) is less natural in most general contexts. The article makes it sound like a normal, complete object.

Often both can mean floor, but there’s a nuance:

• el piso is very common in Latin America for the floor inside a building.
• el suelo can mean the ground/soil, and also “floor,” but it often feels more general (and in some contexts more like “ground”).
  For mopping/cleaning inside a home, el piso is especially common.

Because the sentence begins with a dependent time clause:

• Mientras la plomera estaba trabajando, ... In Spanish (like English), it’s standard to use a comma when you start with that kind of introductory clause. If you reverse the order, the comma is often omitted:
• Yo estaba limpiando el piso con un trapo mientras la plomera estaba trabajando.

Yes, and it changes the feel:

• Mientras la plomera trabajaba, yo limpiaba el piso... (more neutral, less “in the middle of”)
• Mientras la plomera estaba trabajando, yo limpié el piso... (suggests your cleaning was a single completed action during that time, not necessarily ongoing)
• Cuando la plomera estaba trabajando, yo estaba limpiando... (with cuando, it can sound like “when/whenever,” depending on context)

In many Latin American regions, yes:

• trapear = to mop (often specifically with a mop, but sometimes loosely for floor-cleaning) So yo estaba trapeando can sound very natural and shorter.
  However, limpiar el piso con un trapo is perfectly correct and specifically says you used a rag, not necessarily a mop.