La dureza del agua afecta al filtro de agua.

Because Spanish normally contracts these combinations:

• de + el = del
• a + el = al

So:

• de el agua → del agua
• a el filtro → al filtro

These contractions are standard and usually required.

Great question. Agua is indeed a feminine noun.

However, in the singular, some feminine nouns that begin with a stressed a- sound use el instead of la for pronunciation reasons. So you say:

• el agua
• el águila
• el hacha

But they are still feminine. You can see that in agreement:

• el agua fría, not el agua frío

So del agua comes from de + el agua, even though agua is feminine.

Because dureza is a feminine noun.

It means hardness and comes from duro / dura (hard). The ending -eza often forms abstract nouns in Spanish, and many of them are feminine, so:

• la dureza = hardness

Because the subject is singular: La dureza del agua.

Even though that subject contains several words, the main noun is dureza, which is singular. So the verb must also be singular:

• La dureza del agua afecta...

If the subject were plural, the verb would be plural too.

Because the verb afectar is commonly used with a before the thing or person that is affected:

• afectar a algo
• afectar a alguien

So:

• afecta al filtro = affects the filter

For learning purposes, it is best to remember the pattern afectar a.

Because filtro de agua usually means water filter as a type or function: a filter for water.

Compare:

• filtro de agua = water filter / a filter used for water
• filtro del agua = the water’s filter or the filter of the water, which sounds more specific and less natural here

In this sentence, filtro de agua is the normal choice.

Spanish uses the definite article more often than English, especially with:

• abstract nouns
• general concepts
• things being discussed in a general, known sense

So la dureza del agua sounds natural and complete.

You may sometimes see dureza del agua without la in titles, labels, charts, or technical headings, but in a normal sentence la dureza del agua is the standard form.

Yes, very much so.

The structure is:

• La dureza del agua = subject
• afecta = verb
• al filtro de agua = object/complement

So it follows the same basic order as English:

• The hardness of the water affects the water filter.

That makes this sentence quite friendly for an English speaker.

In the plural, it goes back to the normal feminine article:

• singular: el agua fría
• plural: las aguas frías

So the special use of el only happens in the singular before that stressed a- sound.

Not if you want to keep the same meaning.

• al filtro = the filter
• al filtro de agua = the water filter

The second agua tells you what kind of filter it is. Without it, the sentence becomes less specific.