Learn Hardcore Croatian: Usput provjeri je li autobus već stigao. - On the way, check if the bus has already arrived.

Usput literally means “along the way / in passing / while you’re at it.” Putting it first sets the “by the way” context for the whole sentence.
You can also move it: Provjeri usput je li autobus već stigao. The meaning stays similar; starting with Usput just sounds natural and frames it as an extra, quick task.

Why is provjeri used here? What form is it?

Provjeri is the imperative (command), 2nd person singular of provjeriti (to check). It’s telling one person informally: “Check …”
If you’re speaking formally to one person or to multiple people, you’d typically use provjerite.

Is there a difference between provjeri and something like provjeravaj?

Yes—this is about aspect.

provjeri (from provjeriti, perfective) suggests one completed check: “check (once) and find out.”
provjeravaj (from provjeravati, imperfective) suggests ongoing or repeated checking: “keep checking / check regularly.”
In this sentence, a single check is what’s intended, so provjeri fits best.

How does work? Is it the same as ?