Groma viam rectam dirigit.

Because groma is in the nominative singular, the case normally used for the subject of a sentence.
By contrast, viam and rectam are accusative singular forms, so they belong to the object phrase.

In Latin, endings usually tell you each word’s job more clearly than word order does.

Because it is the accusative singular of via.

For a first-declension noun like via:

• via = nominative singular
• viam = accusative singular

Here viam is the direct object of dirigit, so it takes the accusative.

Because rectam is an adjective modifying viam, and Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

Since viam is feminine, singular, accusative, rectam must also be feminine, singular, accusative.

It describes the road.

Rectam is an adjective, so it modifies viam. The phrase means a straight road or the straight road, not directs straight.

If Latin wanted an adverb modifying the verb, it would use a different form, such as recte.

Because Latin is much freer than English about adjective placement. An adjective can come before or after the noun.

So both of these are possible in Latin:

• viam rectam
• rectam viam

The endings make the relationship clear either way.

Dirigit is a present indicative active, third person singular verb form.

That means:

• present = the action is presented as current or general
• indicative = it is a statement
• active = the subject performs the action
• third person singular = he/she/it directs

Since groma is the subject, the sense is it directs.

The -t tells you the verb is third person singular in the present tense.

So dirigit means:

• he directs
• she directs
• it directs

Here it is it directs, because the subject is groma.

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

So:

• groma can mean a groma or the groma
• viam rectam can mean a straight road or the straight road

English has to choose an article, but Latin usually leaves that to context.

No. Latin word order is much more flexible than English word order.

Groma viam rectam dirigit is a perfectly normal sentence, especially with the verb at the end, but Latin could also say:

• Groma rectam viam dirigit
• Viam rectam groma dirigit
• Rectam viam groma dirigit

The endings still show who is doing the action and what receives it. Changes in order usually affect emphasis, not the basic meaning.

Yes, groma is a feminine first-declension noun. Many first-declension nouns are feminine and have -a in the nominative singular.

Its grammatical gender is feminine even though the thing itself is an instrument. In Latin, grammatical gender does not always match biological sex or natural gender.

A rough Classical pronunciation would be:

GRO-ma WEE-am REK-tam DI-ri-git

A few helpful points:

• g is always hard, as in go
• v is pronounced like English w in Classical Latin
• c is always hard, though there is no c in this sentence
• the stress is roughly on GRO, VI, REC, and DI

So viam sounds more like WEE-am than modern English vee-am in reconstructed Classical pronunciation.