Mane via ad forum patet, sed vespere ea saepe turba et plaustris completur.

Because Latin often uses simple adverbial forms to express time.

• mane = in the morning
• vespere = in the evening

So Latin does not need something like in here. English says in the morning, but Latin can simply say mane.

Ad takes the accusative and usually means to, toward, or up to.

So via ad forum means the road to the forum or the road leading toward the forum.

Here forum is accusative singular because it follows ad.

The subject is via.

• via = road/street
• patet = is open / lies open / is accessible

So the first clause is built around via patet: the road is open.
The phrase ad forum simply describes which road it is: the road to the forum.

Patet is from pateo, patere, meaning to be open, to lie open, or to stand open.

In this sentence it does not mean that someone is actively opening the road. It means the road is open or clear/open for passage.

So patet has a slightly more natural Latin feel than a more literal is opened idea.

Ea means it or that one, and it refers back to via.

Why feminine singular?

• via is feminine singular
• ea is the feminine singular form of the pronoun

So in the second clause, ea = that road / it.

Latin often can leave out a word if it is obvious, but it can also restate it with a pronoun for clarity or emphasis.

So ea helps make the structure very clear:

• in the morning, the road is open
• but in the evening, it is often filled...

It is a natural way to connect the two clauses.

Completur is the present passive of compleo, complere, meaning to fill.

• active: aliquis viam complet = someone fills the road
• passive: via completur = the road is filled

Here the road is receiving the action, so Latin uses the passive: ea saepe ... completur = it is often filled.

They go with completur and express what the road is filled with.

Latin commonly uses compleo with the ablative of the thing filling something:

• turbā = with a crowd
• plaustrīs = with carts/wagons

A very important detail: without macrons, turba could look like nominative singular, but here it is really turbā, ablative singular.

So the phrase means filled with a crowd and carts.

Because turba and plaustris are not the subject.

The subject is still ea = the road. That is singular, so the verb is singular:

• ea ... completur = it is filled

The words turbā et plaustrīs tell us with what it is filled.

Latin word order is much freer than English word order.

Saepe means often, and it modifies completur. Its position between ea and turba et plaustris is perfectly normal Latin style.

So the clause means:

• ea saepe ... completur = it is often filled...

The placement may sound unusual in English, but it is natural in Latin.

Yes. Sed means but, and it marks a contrast between the two times of day:

• mane: the road is open
• vespere: the road is often crowded/filled

So sed neatly highlights the change from morning to evening.

No. Classical Latin does not have a definite article like English the.

So:

• via can mean road, a road, or the road
• forum can mean forum, a forum, or the forum

You decide from context which English wording is best.