Learn Hardcore Russian: Светофор помогает водителям безопасно проезжать перекрёстки на оживлённой улице. - The traffic light helps drivers cross busy intersections safely.

кому? — водителю (sg.), водителям (pl.)
делать что? — проезжать (infinitive) The core pattern is: помогать + Dative (person) + Infinitive (action).

Why is the verb in the imperfective infinitive проезжать and not perfective проехать?

The sentence states a general/habitual fact, so the imperfective проезжать fits. Using the perfective проехать would highlight a single completed crossing (e.g., in a specific situation). Both are possible; the aspect just changes the nuance:

General ability/habit: помогает … проезжать
One-time successful result: поможет … проехать

What case and number is перекрёстки, and why plural?

It’s accusative plural of an inanimate noun. Inanimate masculine nouns have the same form in nominative and accusative plural, hence перекрёстки. The plural here is “generic plural,” referring to intersections in general. Singular would be перекрёсток.

Do we need через before перекрёстки?

No. Both are correct:

проезжать перекрёсток (idiomatic and common)
проезжать через перекрёсток (adds the explicit idea of “across/through”) Meaning is essentially the same; choose based on style or emphasis.

Why is it на оживлённой улице (prepositional) and not на оживлённую улицу (accusative)?

Because it answers “where?” (location), not “to where?” (destination). With на:

Location (где?): на оживлённой улице (prepositional)
Direction (куда?): на оживлённую улицу (accusative)

Which word does на оживлённой улице modify here?

By default, it most naturally attaches to the noun right before it, i.e., перекрёстки (“intersections on a busy street”). If you want it to set the overall scene rather than modify “intersections,” move it to the front:

На оживлённой улице светофор помогает водителям… If you want to be precise about intersections of busy streets, say:
…проезжать перекрёстки оживлённых улиц.

Why does оживлённой end in -ой? Is that prepositional or instrumental?

For feminine long-form adjectives, both prepositional and instrumental can end in -ой/-ей. The preposition tells you the case:

на оживлённой улице = prepositional (location)
с оживлённой улицей = instrumental (with) Notice the noun endings differ: улице (prep) vs улицей (instr.).

What’s going on with the spelling/pronunciation зж in проезжать?

In verbs like проезжать/въезжать/переезжать, you see зж, which is pronounced like a long “zh” sound [жж]. So проезжать is pronounced as if “проежжать,” but is correctly spelled with зж.

Where is the stress in the key words?

светофо́р
помога́ет
води́телям
безопа́сно
проезжа́ть
перекрёстки (ё is always stressed)
оживлённой (ё is always stressed)
у́лице

Why is светофор singular? Are we talking about one traffic light or traffic lights in general?

Russian often uses the singular as a generic subject. Светофор помогает… means “Traffic lights help…” in general. You can also use plural: Светофоры помогают…—both are fine.

What exactly does безопасно do here, and can I move it?

Безопасно is an adverb modifying проезжать (“to cross safely”). Word order is flexible:

безопасно проезжать (neutral)
проезжать безопасно (slight emphasis on how they cross) Note: в безопасности means “in safety/safe,” not the same as the adverb.

Is any comma needed in this sentence?

No. It’s a single simple clause with no parenthetical or subordinate parts, so no comma is required.