Parentes pueros et puellas bonos mores docent.

This is a very common Latin pattern with docere: it can take two accusatives.

• pueros et puellas = the people taught
• bonos mores = the thing taught

So the sentence literally works like:

Parents teach boys and girls good morals / good manners.

This is called the double accusative with docere.

No. Bonos goes with mores, not with pueros et puellas.

You can tell because:

• bonos is masculine accusative plural
• mores is also masculine accusative plural

But puellas is feminine, so bonos cannot be describing puellas. The phrase is bonos mores = good manners.

Because mores is a masculine plural noun. Adjectives have to agree with the noun they describe in gender, number, and case, so the adjective must also be masculine plural accusative:

• mores = masculine accusative plural
• bonos = masculine accusative plural

So bonos mores is the correct agreement.

Docent is:

• 3rd person plural
• present tense
• active voice
• indicative mood

It comes from doceo, docere, meaning to teach.

So docent means they teach.

Because Latin does not need it here. English often uses to with teach, but Latin usually does not. With docere, the person taught is often put directly into the accusative, without a preposition.

So Latin says literally:

Parents teach boys and girls good manners,
not Parents teach good manners to boys and girls with a special word for to.

Yes. Latin word order is much freer than English word order because the endings show how the words function.

So these could still mean the same thing:

• Parentes pueros et puellas bonos mores docent.
• Bonos mores parentes pueros et puellas docent.
• Pueros et puellas parentes bonos mores docent.

The exact order can change for emphasis, but the case endings still show:

• parentes = subject
• pueros et puellas = people taught
• bonos mores = thing taught

Because Latin has no articles. There is no direct equivalent of English the, a, or an in ordinary Latin.

So parentes can mean:

• the parents
• parents

and the exact sense depends on context.

Yes. Parentes is a plural noun meaning parents, and it can refer either to:

• a particular set of parents, depending on context, or
• parents in general

In a sentence like this, it often sounds like a general statement: Parents teach boys and girls good manners.