Пятновыводитель и кондиционер для белья находятся рядом.

Because the subject is made of two nouns joined by и: пятновыводитель и кондиционер.

Even though each noun is singular by itself, together they form a plural subject, so the verb is plural:

• пятновыводитель находится = the stain remover is located
• пятновыводитель и кондиционер находятся = the stain remover and the conditioner are located

Находятся means are located / are situated.

In Russian, the present tense of to be is usually not stated in simple sentences, so есть is generally not used here the way English uses are. In fact:

• Пятновыводитель и кондиционер для белья рядом.
  = perfectly possible in everyday speech, more concise
• Пятновыводитель и кондиционер для белья находятся рядом.
  = more explicit, a bit more formal or descriptive

So находятся adds the idea of location.

Рядом means nearby, close, next to.

It can be used in two main ways:

• рядом by itself = nearby / close together
• рядом с + instrumental = next to something specific

For example:

• Они рядом. = They are next to each other / close by.
• Они рядом с окном. = They are next to the window.

In your sentence, nothing follows рядом, so с is not needed. With two items as the subject, рядом often naturally means next to each other.

Белья is genitive singular.

That is because the preposition для always takes the genitive:

• для белья = for laundry / for clothes / for linen

The base form is бельё.
So:

• nominative: бельё
• genitive: белья

In this sentence, бельё means laundry.

Depending on context, бельё can also mean:

• linen
• underwear
• bed linen

But in кондиционер для белья, the standard meaning is fabric softener / laundry conditioner, so бельё is best understood as laundry here.

Grammatically, it most naturally modifies only кондиционер:

• пятновыводитель
• и кондиционер для белья

So the phrase is understood as:

• stain remover
• and fabric conditioner

If you wanted for laundry to apply clearly to both items, Russian would usually rephrase it, for example:

• пятновыводитель для белья и кондиционер находятся рядом
• or средства для белья находятся рядом

Yes, in this context.

The word кондиционер has several meanings in Russian, just like conditioner in English. It can mean:

• air conditioner
• hair conditioner
• fabric conditioner / fabric softener

The phrase кондиционер для белья makes the meaning clear: it is the laundry product, not an air conditioner.

More or less yes, but it helps to see how it is built.

It comes from parts meaning roughly:

• пятно = stain
• выводить = to remove, to get out
• -тель = a common noun-forming ending for a thing that does something

So пятновыводитель literally means something like stain-remover.

Russian often forms practical compound words like this. You should learn it as one vocabulary item, but recognizing the parts makes it easier to remember.

Yes, often you could.

Russian commonly uses posture/location verbs:

• стоят = are standing
• лежат = are lying
• висят = are hanging
• находятся = are located

So if the bottles are standing on a shelf, стоят рядом may sound very natural.
If the objects are just being located without focusing on position, находятся рядом is neutral and safe.

No, Russian word order is fairly flexible.

The sentence as written is neutral:

• Пятновыводитель и кондиционер для белья находятся рядом.

You could also say:

• Рядом находятся пятновыводитель и кондиционер для белья.

That version emphasizes the location a bit more, like Nearby are the stain remover and the fabric conditioner.

So the original order is standard, but not the only possibility.

Here are the key stress patterns:

• пятновыводи́тель
• кондиционе́р
• бельё
• нахо́дятся
• ря́дом

A few useful notes:

• ё is always stressed, so бельё is pronounced roughly byel-YO
• нахо́дятся has stress on хо
• ря́дом has stress on the first syllable

If you learn the stress together with the word, your Russian will sound much more natural.