Dans la salle de bains, il y a une baignoire blanche et un radiateur sous la fenêtre.

This phrase sets the location first: Dans la salle de bains = In the bathroom.

French often puts a place phrase at the beginning of a sentence when it wants to establish the setting before saying what is there. You could also say:

Il y a une baignoire blanche et un radiateur sous la fenêtre dans la salle de bains.

That is grammatically possible, but the original version sounds more natural if the speaker wants to start with the room itself.

Dans usually means in or inside something specific.

So:

• dans la salle de bains = in the bathroom

En can also mean in, but it is used in different situations, for example:

• en France
• en voiture
• en été

For a room or an enclosed space like a bathroom, dans is the normal choice.

Il y a means there is or there are.

It is the standard French way to say that something exists or is present somewhere.

So:

• il y a une baignoire = there is a bathtub
• il y a une baignoire et un radiateur = there is a bathtub and a radiator / there are a bathtub and a radiator

Even though English switches between there is and there are, French uses il y a for both singular and plural:

• Il y a un livre.
• Il y a deux livres.

This is a fixed expression in French: la salle de bains means the bathroom.

Literally, it is something like the room for baths, which helps explain the plural bains.

You may also see salle de bain in modern usage. Both exist, but salle de bains is very common and completely standard.

In French, most adjectives come after the noun.

So:

• une baignoire blanche = a white bathtub

That is the normal word order.
A small group of common adjectives often come before the noun, such as:

• grand
• petit
• beau
• jeune
• vieux

But color adjectives like blanc / blanche usually come after the noun.

Because baignoire is a feminine noun.

French adjectives must agree with the noun they describe in gender and number:

• masculine singular: blanc
• feminine singular: blanche
• masculine plural: blancs
• feminine plural: blanches

So:

• un radiateur blanc
• une baignoire blanche

Because French nouns have grammatical gender.

• baignoire is feminine, so it takes une
• radiateur is masculine, so it takes un

This does not mean that the objects themselves are feminine or masculine in any real-world sense. It is simply a grammatical feature of the noun, and you usually have to learn the gender together with each noun.

La fenêtre means the window.

French often uses the definite article where English might also use the, especially when the thing is understood from the context. In a bathroom, if there is one relevant window being referred to, sous la fenêtre means under the window.

If you said sous une fenêtre, it would mean under a window, which sounds less specific.

Because French does not need to repeat il y a when listing things.

So:

• Il y a une baignoire blanche et un radiateur
  means
• There is a white bathtub and a radiator

French can use one il y a for the whole list.
You could repeat it, but it would usually sound heavier and less natural:

• Il y a une baignoire blanche et il y a un radiateur...

Usually, yes. In a sentence like this, un radiateur is the heater attached to the wall, often below a window.

So un radiateur sous la fenêtre is very naturally a radiator under the window.

The comma separates the opening location phrase from the main statement:

• Dans la salle de bains, = setting
• il y a une baignoire blanche... = main information

This kind of comma is common when a sentence begins with a phrase giving place, time, or context. It helps readability, though punctuation can vary a little depending on style.

Not naturally in this case.

Use il y a to say that something is present or exists somewhere:

• Dans la salle de bains, il y a une baignoire blanche...

Use c'est to identify or present something:

• C'est une baignoire blanche. = It's a white bathtub.

So in this sentence, il y a is the correct choice because the speaker is describing what the bathroom contains.

You would make the noun plural:

• Dans la salle de bains, il y a une baignoire blanche et des radiateurs sous la fenêtre.

Key changes:

• un radiateur → des radiateurs

Notice that il y a stays the same, even with a plural noun.