La fontanera dijo que hay que cambiar la cisterna del baño.

Because fontanera is the feminine form of fontanero, so it tells you the plumber is a woman.

• el fontanero = a male plumber
• la fontanera = a female plumber

In Spain, fontanero/a is the usual word for plumber. In some Latin American countries, you may hear plomero/a instead.

Spanish usually uses the definite article when talking about a specific person with a profession or role:

• La fontanera dijo... = the plumber said...

In English, we also say the plumber, so this part matches quite well.

A useful contrast:

• Es fontanera = She is a plumber.
  Here there is no article, because you are just naming her profession.
• La fontanera llegó = The plumber arrived.
  Here it is a specific person, so the article is used.

Dijo is the preterite of decir, and que introduces the reported statement.

So the structure is:

• dijo = said
• que = that

Spanish normally keeps que after verbs like decir, pensar, creer, explicar, etc., when introducing a full clause. English sometimes drops that, but Spanish usually does not:

• Dijo que hay que cambiar...

That is the normal way to report what someone said.

Dijo is the preterite, which presents the act of speaking as a completed event in the past.

• dijo = she said
• decía = she was saying / used to say
• ha dicho = she has said

In this sentence, dijo sounds like a simple past report of what the plumber said at a particular moment.

A rough contrast:

• La fontanera dijo que... = She said it.
• La fontanera decía que... = She kept saying / was saying...
• La fontanera ha dicho que... = She has said..., often with stronger connection to the present.

In much of Spain, ha dicho is also common for recent past events, but dijo is perfectly natural.

Hay que + infinitive is a very common impersonal structure meaning something like:

• it is necessary to...
• one must...
• ...needs to be...

It does not say exactly who has to do it. That is why it works well when the focus is on the necessity of the repair, not on the person responsible.

Compare:

• Hay que cambiar la cisterna = The cistern needs to be changed / It’s necessary to change the cistern.
• Tenemos que cambiar la cisterna = We have to change the cistern.
• Tienen que cambiar la cisterna = They have to change the cistern.

So hay que is more general and less personal.

Because after hay que, Spanish uses an infinitive.

This is a fixed pattern:

• hay que cambiar
• hay que arreglar
• hay que llamar
• hay que limpiar

So once you see hay que, you should expect the next verb to be in the infinitive.

Because this is a straightforward reported statement, so Spanish uses the indicative.

The plumber is stating something as a fact or necessity:

• dijo que hay que cambiar...

There is no trigger here that requires the subjunctive.

A useful comparison:

• Dijo que hay que cambiar la cisterna.
  She said that the cistern needs to be changed.

• Dijo que cambiáramos la cisterna.
  She told us to change the cistern.

In the second sentence, cambiáramos is subjunctive because the meaning has changed: it is now more like a command or instruction.

In this context, cisterna means the toilet cistern / toilet tank, especially in Spain.

That is important because cisterna can also mean a tank or reservoir in other contexts. But in a bathroom sentence like this, it normally refers to the tank attached to the toilet.

Related words in Spain:

• inodoro = toilet
• váter = toilet / loo
• cisterna = the tank/cistern part of the toilet

So cisterna is usually not the whole toilet.

Because de + el contracts to del in Spanish.

So:

• de el baño → del baño

This contraction is mandatory.

The only common exception is when el is part of a proper name:

• de El Escorial
  But that does not apply here.

Literally, it means of the bathroom, but Spanish often uses de + noun where English prefers a noun-noun combination.

So la cisterna del baño is a natural Spanish way to refer to the bathroom cistern or, more naturally in English, the toilet tank in the bathroom.

In real life, many speakers might also say:

• la cisterna del inodoro
• la cisterna del váter

Those are a bit more specific, because the cistern belongs to the toilet, not to the whole bathroom. But del baño is still understandable and natural enough in context.

Yes. If you want to say who has to do it, you would replace hay que with a personal expression.

For example:

• La fontanera dijo que tenemos que cambiar la cisterna del baño.
  The plumber said that we have to change it.

• La fontanera dijo que tienen que cambiar la cisterna del baño.
  The plumber said that they have to change it.

• La fontanera dijo que se tiene que cambiar la cisterna del baño.
  A more impersonal/passive-like option: the cistern has to be changed.

So hay que is chosen when the speaker wants to keep things general.

This is the normal, neutral word order.

• La fontanera dijo que hay que cambiar la cisterna del baño.

Spanish can change word order for emphasis, but the standard order here is very natural:

1. subject: La fontanera
2. verb: dijo
3. reported clause: que hay que cambiar la cisterna del baño

You could move parts around in special contexts, but for everyday speech and learning purposes, this version is the one to copy.