Vectura et mutuum mercatori utilia sunt.

Because they are joined by et and together make a compound subject: vectura et mutuum = transport and a loan.

In Latin, just as in English, two singular nouns joined by and usually take a plural verb.

• vectura = singular
• mutuum = singular
• vectura et mutuum = plural in sense

So Latin uses sunt = are, not est = is.

They are both nominative singular, because each one is a subject of the sentence.

• vectura = nominative singular
• mutuum = nominative singular

Even though the whole subject is plural in meaning because there are two items, each noun itself stays singular because each names one thing.

Because utilis/utile often takes the dative for the person something is useful, helpful, suitable, and so on.

So:

• mercator = merchant
• mercatori = to/for the merchant

In this sentence, mercatori means to the merchant or for the merchant.

This is a very common Latin pattern:

• alicui utilis est = it is useful to someone

So mercatori utilia sunt literally means they are useful to the merchant.

Because it is the predicate adjective with a compound subject, and that subject contains nouns of different genders:

• vectura is feminine
• mutuum is neuter

When Latin has a plural idea made up of non-personal things of mixed gender, it often uses the neuter plural for the adjective. So utilia agrees with vectura et mutuum taken together.

So the grammar is:

• vectura et mutuum = the combined subject
• utilia = useful, nominative neuter plural
• sunt = are

Because utilia describes both nouns together, not just one of them.

If Latin wanted to describe each noun separately, it might have to phrase things differently. But here the idea is:

• both transport and a loan are useful

Since the meaning is plural, the adjective is plural too.

Here are the main forms:

• vectura — noun, vectura, -ae (feminine)
• et — conjunction, and
• mutuum — noun, mutuum, -i (neuter), loan
• mercatori — from mercator, mercatoris (masculine), merchant
• utilia — from utilis, utile, useful
• sunt — from sum, esse, are

So a learner should recognize that several words appear in forms different from their dictionary form:

• mercatori is from mercator
• utilia is from utilis, utile
• sunt is from sum

Yes, here it is a noun meaning loan.

Latin often uses forms that look adjectival as nouns when the context makes the meaning clear. In this sentence, mutuum is one of the two subjects, alongside vectura, so it is functioning as a noun.

That is why the sentence means something like:

• Transport and a loan are useful to the merchant

not

• Transport and borrowed... are useful...

Because Latin does not have articles like English the and a/an.

So a Latin noun like mercator or mutuum can mean:

• the merchant / a merchant
• the loan / a loan

The exact sense depends on context. English has to choose an article, but Latin usually does not mark that distinction.

Not as much as it would be in English. Latin word order is fairly flexible because the endings show the grammar.

So this sentence could be rearranged in other ways without changing the basic meaning, for example:

• Mercatori vectura et mutuum utilia sunt
• Vectura et mutuum utilia mercatori sunt

The given order is perfectly normal, but the roles are understood mainly from the forms:

• mercatori is dative
• utilia is nominative plural
• sunt is the verb

A simple way to break it down is:

• Vectura et mutuum = subject
• mercatori = dative with utilia
• utilia = predicate adjective
• sunt = verb

So the sentence is built like this:

[subject] + [dative of person concerned] + [predicate adjective] + [verb]

Or more literally:

Transport and a loan are useful to the merchant.