El acta de entrega incluye la lectura del contador.

Because acta is a feminine noun that begins with a stressed a sound. In singular, Spanish uses el instead of la before that kind of noun to make pronunciation smoother.

So:

• el acta
• el agua
• el alma

But the noun is still feminine. You can see that with adjectives:

• el acta firmada
• el acta oficial

And in the plural, it goes back to las:

• las actas

Not usually. Acta is a false friend here.

In administrative or legal Spanish, acta usually means something like:

• record
• report
• certificate
• minutes
• official document

So acta de entrega is not an act of delivery in normal English. It is more like a handover record, delivery record, or handover certificate, depending on context.

Here de entrega identifies the type or purpose of the document.

Spanish often uses:

• noun + de + noun

where English often prefers:

• a compound noun, or
• an adjective-like noun

So:

• acta de entrega = literally record of handover/delivery
• natural English = handover record or delivery record

The de is simply linking the two nouns.

Because acta de entrega works as a set administrative expression naming a type of document.

In Spanish, when a de phrase is being used more like a label or category, the article is often omitted:

• acta de entrega
• carta de presentación
• libro de texto

If you said acta de la entrega, that would sound more like the record of the specific handover, with more emphasis on a particular event. In many official contexts, acta de entrega is the standard fixed phrase.

Because the subject is singular: El acta de entrega.

The verb comes from incluir and here it is in the third person singular present:

• el acta ... incluye

Compare:

• El acta incluye... = singular
• Las actas incluyen... = plural

So the verb agrees with acta, not with lectura.

Yes, literally lectura means reading, but in this context it has a more specific administrative/technical meaning.

With a meter, la lectura means:

• the value shown on the meter
• the recorded meter reading

So la lectura del contador is the standard way to say the meter reading.

It does not mean someone is sitting there reading something like a book.

Because de + el contracts to del in Spanish.

So:

• de + el contador → del contador

This contraction is mandatory in normal Spanish.

Compare:

• del contador = de + el contador
• de la factura = no contraction, because de + la does not contract

In other contexts, yes. Contador can mean different things depending on the situation, including:

• meter
• counter
• accountant in some varieties or contexts

But here, lectura del contador makes it clear that contador means meter. A meter is something you take a reading from.

In Spain, this is very common in utility or property contexts:

• contador de agua = water meter
• contador de luz = electricity meter
• contador de gas = gas meter

Spanish generally uses definite articles more often than English does.

In this sentence, each noun is presented as a specific, identifiable thing:

• el acta de entrega = the specific handover document
• la lectura = the specific reading
• del contador = of the specific meter involved

English sometimes drops articles in labels or headings, but Spanish usually keeps them in a full sentence like this.

Yes. A very natural alternative would be:

La lectura del contador está incluida en el acta de entrega.

That means essentially the same thing.

The difference is mainly focus:

• El acta de entrega incluye... focuses first on the document
• La lectura del contador está incluida... focuses first on the meter reading

Both are correct and natural.