Learn Russian: Они же наверняка опоздают, вряд ли автобус придёт вовремя. - They will certainly be late; it is unlikely the bus will arrive on time.

Here, же adds emphasis and appeals to shared knowledge or obviousness. It makes the statement feel like 'But they will definitely be late (and we both know this).' It adds an emotional tone of frustration or absolute certainty that just saying Они наверняка опоздают wouldn't have.

How exactly does the phrase вряд ли work here?

вряд ли is a fixed phrase used to express doubt, meaning 'hardly' or 'it is unlikely that'. Notice that it doesn't need a connecting word like 'that' (что) in Russian; you just put it directly before the phrase it modifies, as in вряд ли автобус придёт (it is unlikely the bus will arrive).

Why use придёт (will walk/come) for a bus instead of приедет (will arrive by vehicle)?

While buses are obviously vehicles, Russians commonly use verbs of motion on foot like идти or прийти for scheduled public transport (buses, trains, trams) when talking about them arriving or running on a route. You can use приедет, but придёт is very natural and standard here.

Why is опоздают in the perfective aspect?

опоздают is the future perfective form of опоздать (to be late). We use the perfective aspect because the speaker is talking about a specific, one-time result in the future: the singular event of them missing their deadline or arriving late on this particular occasion.