It is a feature of English nouns that they can be placed before another noun, and there is no hard and fast distinction between a noun and a noun modifier, nor indeed between a noun with a noun modifier and a compound noun. In some cases it seems clear to everyone that a unit is a compound noun, while in others the edges are fuzzy, especially when the combination is open rather than hyphenated or closed. If you look at the Macmillan English Dictionary (MED), you will see that floor show and floor lamp, for example, are given their own place as compound noun headwords, but floor covering isn’t.

In fact, none of the dictionaries I have looked at gives floor covering as a compound, so I’d be inclined to say it is a noun – covering – modified by another noun – floor. But there is no absolute reason why floor covering shouldn’t be regarded as a compound noun: it is reasonably frequent, and it can be pluralized and can be the subject or object of a sentence. You could say any of these sentences:

I like the new floor covering.
Fashions in floor coverings change frequently.
The present floor covering will make the rest of the building took tatty.

So it’s really up to you whether you want to call it one (compound) noun or two nouns, with one of them behaving as a modifier.

Some nouns are used so frequently as modifiers that they are actually classified as adjectives: for example, in MED, family is classed both as a noun and an adjective. Feline quadruped comes into this category, because although feline is a noun (Lions are felines) it is also classified by most dictionaries (including MED) as an adjective too. So I’d say that what you have here is a noun modified by an adjective, rather than two nouns.

You can see why lexicographers spend a lot of time debating whether to classify a particular item as a noun or an adjective, or whether a particular combination qualifies as a compound noun or is just one noun premodified by another.

Is the following sentence correct?
The storm came so unexpected that we didn't have enough time to make any preparation.

Most people would regard The storm came so unexpected … as incorrect, because unexpected is an adjective, whereas what is needed here is an adverb: The storm came so unexpectedly … It would be correct to say The storm was so unexpected … because a few verbs like be, feel, look and seem are followed by an adjective rather than an adverb.

People do use adjectives when strictly speaking an adverb is required, especially in informal speech. Some common adjectives have been used so frequently in this way that they are now classified as adverbs as well, though they are often labelled as ‘spoken’ or ‘informal’. So you can say Don’t talk so loud or He walks too quick – both of these words are classed as both adjective and adverb in the Macmillan English Dictionary and other learners’ dictionaries. The fact that they are regarded as informal means that you should probably avoid using them in careful writing.

There are two other minor changes that I would make to the sentence: I would add on after came, to make it more idiomatic, and I would make preparations plural (you could also say we didn’t have time to prepare ourselves).

I was wondering if the word fountainside is one word or two words? I have been arguing with someone about this.

As you probably know, there are no hard and fast rules governing when a compound noun stops being two words and decides to become one (sometimes going through a hyphenated phase along the way). Over the centuries many nouns have fused with other nouns so firmly that we no longer think of them as two. Good examples here are words like seaside, riverside, and lakeside, all of which are now generally written as one word. Indeed, there are hundreds of citations for the closed forms of these words in the corpus on which the Macmillan English Dictionary is based, and hardly any for the open forms.

Fountainside does not strike us as a natural combination in the way that those other words do simply because it’s not that frequent – we often talk and write about being beside a river, a lake or the sea, but not often about being beside a fountain. There are no citations at all in the corpus for either fountainside or fountain side, but if you do a search on Google you will find roughly 50,000 for the closed form and 15,000 for the open form. (Not all of these are relevant, of course, but it gives an idea.) So I’d say you are justified in writing it either closed or open as you choose. It’s probably not worth arguing about, though.