Learn Spanish (Latin America): Hay una alfombra azul en la sala.

Hay means "there is" or "there are". We use it to talk about the existence of something, especially unspecific things like "a rug" (una alfombra). We use está when we want to say where a specific thing is located, like "the rug is in the living room" (la alfombra está en la sala).

Can hay also mean "there are" if there is more than one rug?

Yes! Hay is a very useful word because it never changes shape for singular or plural. It means both "there is" and "there are". If you wanted to say "There are two blue rugs", you would just say Hay dos alfombras azules.

Why does the color come after the object (alfombra azul instead of azul alfombra)?

In Spanish, descriptive words (adjectives) almost always come after the noun they describe. You first state the thing you are talking about (alfombra), and then you give more information about it (azul).

Since alfombra is a feminine word, shouldn't the color change to match it, like azula?

Adjectives that end in a consonant, like azul, don't change to match the gender of the noun. They use the exact same form for both masculine and feminine words. You only change them if you need to make them plural (by adding -es, like azules).