Learn Russian: Простите, я сейчас работаю.

Russian does not have a separate "-ing" form for actions happening right now, and you never use a translation for "am" here. The single present tense verb работаю covers both "I work" (in general) and "I am working" (right now).

Why does простите end in -те?

The -те ending shows that you are being polite (formal) or speaking to more than one person. If you were saying sorry to a close friend, family member, or a child, you would use the informal version: прости.

Is there a difference between простите and извините?

They are very similar and often used interchangeably. Извините is slightly more like "excuse me" (like when trying to get past someone), while простите can feel a bit more apologetic, like "forgive me". However, for an everyday interruption like this, either one works perfectly.

How do native speakers usually pronounce сейчас? It looks like it should be "sey-chas".

While it is spelled сейчас, Russians often speak fast and blend the sounds together. In everyday conversation, it usually sounds more like "see-chas" or even a very quick "shchas". Don't be surprised if the spoken version sounds a bit different from the spelling!