La planta que és al costat de la finestra és de la meva mare.

Because planta is a feminine noun in Catalan, so it takes the feminine article la.

• la planta = the plant
• una planta = a plant

As in many Romance languages, the article has to agree with the noun’s gender.

Here que is a relative pronoun, meaning that or which.

So:

• La planta que és al costat de la finestra
  = The plant that is next to the window

It links la planta to the extra information és al costat de la finestra.

No, not here.

In English, you can sometimes drop that, but only in certain cases, such as The book that I bought → The book I bought.

In this Catalan sentence, que is the subject of the relative clause, so it must stay:

• la planta que és... = the plant that is...

You cannot leave it out.

Catalan often uses ser where English speakers might expect estar, especially when talking about where something is located.

So és al costat de la finestra is natural Catalan for is next to the window.

Very roughly:

• ser is commonly used for location in many normal descriptions
• estar is used more for states, conditions, or sometimes temporary/resulting situations

So this is not a direct match with Spanish or English patterns. In this sentence, és is fine and natural.

Al costat de means next to, beside, or at the side of.

Examples:

• al costat de la finestra = next to the window
• al costat de la porta = next to the door

It is a fixed expression you should learn as a whole.

Because al is the contraction of a + el.

• a + el → al

So:

• al costat literally comes from a el costat

This contraction is standard in Catalan, just like:

• del = de + el

In this sentence, és de la meva mare means belongs to my mother or is my mother’s.

Catalan often uses ser de + person to show ownership:

• És del Joan = It belongs to Joan
• És de la meva mare = It belongs to my mother

So de here expresses possession, not just of in a literal English sense.

In standard Catalan, possessives usually go with the definite article:

• la meva mare = my mother
• el meu pare = my father
• el meu cotxe = my car

This is different from English, which does not use the before my.

So la meva mare is the normal standard pattern.

Because the possessive has to agree with the noun it describes.

Here the noun is mare, which is feminine singular, so the possessive must also be feminine singular:

• el meu pare = my father
• la meva mare = my mother

So:

• meu = masculine singular
• meva = feminine singular

It has two main parts:

• La planta que és al costat de la finestra
  = The plant that is next to the window
• és de la meva mare
  = belongs to my mother / is my mother’s

So the structure is:

[noun] + [relative clause] + [main verb + possession]

That is why the sentence literally works like:

The plant that is next to the window belongs to my mother.

Yes. Planta can mean plant, but in some contexts it can also mean floor/story of a building.

For example:

• Una planta verda = a green plant
• La tercera planta = the third floor

In your sentence, al costat de la finestra makes it clear that planta means plant.