Si ad forum pervenire vis, hic pons tibi transeundus est.

Si means if and introduces a condition.

Here vis is present indicative because this is a straightforward, real condition: If you want to reach the forum... Latin does not need the subjunctive here. A learner may expect something more complicated after if, but this is just the normal way to say a simple condition.

So the first part is:

• si = if
• ad forum pervenire vis = you want to reach the forum

Ad takes the accusative case, so forum here is accusative singular.

The phrase ad forum means to the forum or toward the forum. It shows motion directed to a place.

A native English speaker may wonder why Latin does not just use a bare noun. The reason is that Latin often uses a preposition like ad with the accusative to show movement toward something.

Also, forum is a second-declension neuter noun, so its nominative and accusative singular are both forum.

Because vis comes from velle, to want, and velle commonly takes a complementary infinitive.

So:

• vis = you want
• pervenire = to arrive, to reach

Together, pervenire vis means you want to reach or you want to get to.

This is very similar to English want to go, want to see, want to arrive.

Pervenire means to come through to, to arrive at, or to reach. In this sentence, the natural sense is to get to or to reach the forum.

So ad forum pervenire is not just to go toward the forum, but more specifically to make it there.

That is why the clause means not merely if you want to go to the forum, but more precisely if you want to reach the forum.

Because pons is masculine singular nominative, and hic has to agree with it in gender, number, and case.

So:

• hic = this (masculine nominative singular)
• pons = bridge (masculine nominative singular)

Together: hic pons = this bridge

A learner might expect a different form because pons is a third-declension noun, but it is still masculine, so hic is the correct demonstrative form.

Yes. This is the gerundive used with est, a construction often called the passive periphrastic.

The gerundive expresses necessity or obligation. So transeundus est literally means is to be crossed, and more naturally must be crossed.

So:

• hic pons transeundus est = this bridge must be crossed

This is one of the standard Latin ways to say that something has to be done.

Because the verb is transeo, transire, a compound of eo, ire (to go).

The gerundive of eo is eundus, so compounds of eo form their gerundives the same way:

• eo → eundus
• transeo → transeundus

So transeundus is the expected form from transeo.

This looks strange at first if you are used to verbs making gerundives in -iendus, but eo is irregular, and its compounds keep that irregular pattern.

Tibi is the dative singular of tu, and in this construction it marks the person on whom the necessity rests.

So hic pons tibi transeundus est literally means something like:

• this bridge is to-be-crossed for you
• or better, this bridge must be crossed by you

In natural English, we usually turn that into you must cross this bridge.

This use of the dative is very common with the passive periphrastic.

Because with the passive periphrastic, Latin often uses the dative of agent rather than ab + ablative.

So with ordinary passive verbs, you often get:

• a te = by you

But with a gerundive expressing obligation, Latin very commonly prefers:

• tibi = for you / by you in the sense of obligation resting on you

That is why tibi transeundus est is the idiomatic expression here.

Because the whole expression is grammatically passive.

In an active sentence, you might say:

• hunc pontem transire debes = you must cross this bridge

There, pontem is the direct object.

But in the passive periphrastic, the thing that must be acted on becomes the grammatical subject:

• hic pons tibi transeundus est = this bridge must be crossed by you

So pons is nominative because it is the subject of est.

Yes, that would be perfectly good Latin.

• hunc pontem transire debes = you must cross this bridge
• hic pons tibi transeundus est = this bridge must be crossed by you

The basic meaning is very similar. The difference is mainly in style and structure:

• debes + infinitive is often more direct and easier for beginners.
• the gerundive + est construction is a classic Latin way to express necessity, often a bit more formal or impersonal in feel.

So the sentence you were given uses a very characteristically Latin structure.

Not as much as it would be in English. Latin word order is relatively flexible because the endings show the grammatical relationships.

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

• Si vis ad forum pervenire, hic pons tibi transeundus est.

The given order may help emphasize certain ideas:

• ad forum comes early, so the destination is clear right away.
• hic pons stands prominently as the thing that must be crossed.
• tibi transeundus est places the obligation neatly at the end.

So the word order is meaningful in terms of emphasis, but it is not rigid in the way English word order is.