A veces falta una pinza, así que mi madre guarda otras junto a la fregona.

Because the subject is una pinza, which is singular, so the verb must also be singular: falta.

A useful way to read it is:

• una pinza falta = one clothespin is missing

Spanish often uses faltar this way, where the thing that is missing is the subject.

Not exactly.

• faltar means to be missing / to be lacking
• perder means to lose

So:

• A veces falta una pinza = Sometimes a clothespin is missing
• A veces se pierde una pinza = Sometimes a clothespin gets lost

The sentence with faltar focuses on the result: the clothespin is not there.
The sentence with perderse focuses more on the event of losing it.

Yes, but the meaning would change slightly.

• A veces falta una pinza = Sometimes one clothespin is missing
• A veces faltan pinzas = Sometimes clothespins are missing

The singular version sounds like a typical recurring situation where one is missing. The plural version is more general and less specific.

In this sentence, pinza most likely means a clothespin / clothes peg.

In Spanish, pinza can mean different kinds of clip-like objects depending on context, for example:

• a clothes peg
• a clip
• tongs
• a clamp

Here, because of the everyday household context, pinza is understood as a clothes peg / clothespin.

Because otras is being used as a pronoun, replacing the noun pinzas.

So:

• mi madre guarda otras
  means
• my mother keeps some others

The full version would be:

• mi madre guarda otras pinzas

But Spanish often omits the noun when it is obvious from context.

Also notice the agreement:

• pinza is feminine
• plural = pinzas
• so otras must also be feminine plural

Here guarda means something like keeps or stores.

The verb guardar is very common and can mean:

• to keep
• to store
• to put away
• sometimes to save

In this sentence, mi madre guarda otras means she keeps extra ones somewhere, ready to use.

Así que means so, therefore, or so then.

It connects the first idea to the result or consequence:

• A veces falta una pinza = Sometimes a clothespin is missing
• así que mi madre guarda otras = so my mother keeps others

It is very common in spoken and written Spanish.

Compare:

• porque = because
• así que = so / therefore

So así que introduces the consequence, not the cause.

Junto a means next to, beside, or right by.

So:

• junto a la fregona = next to the mop

Yes, you could also say al lado de la fregona. In many situations, the meaning is almost the same.

A small nuance:

• junto a can sound a little more direct or compact
• al lado de is also very common and natural

Both are correct here.

Because the normal expression is junto a.

• junto a = next to / beside

So you say:

• junto a la puerta
• junto al armario
• junto a la fregona

If the next word is el, it contracts:

• junto a + el = junto al

Example:

• junto al cubo

But with la, there is no contraction:

• junto a la fregona

In Spain, la fregona usually means the mop.

That is a specifically Spain-friendly word. In other Spanish-speaking regions, other words may be more common, such as:

• trapeador
• mopa

So if you are learning Spanish from Spain, fregona is a very useful household word.

Because the sentence describes a habitual or repeated situation.

• A veces falta una pinza = this happens sometimes
• mi madre guarda otras = this is what she usually does in response

Spanish uses the present tense for regular habits and general truths, just like English often does:

• Sometimes one is missing, so my mother keeps others nearby.

So this is not necessarily happening right now; it is a normal repeated situation.