Learn Farsi: معلم جدید خیلی جدیست اما کیف او سبکه. - The new teacher is very serious, but his bag is light.

In spoken and informal Farsi, the "to be" verb است (is) gets shortened. Because the adjective جدی (jeddi, meaning serious) ends in a vowel, the shortened verb becomes ـست (-st). It attaches directly to the word, creating جدیست (jeddist).

In سبکه, how is the verb "is" attached to the word سبک (light)?

The word سبک (sabok) ends in a consonant. In colloquial Tehrani, when است follows a consonant, it shrinks down to just an "e" sound. In writing, this is shown by attaching a silent ـه (heh) to the end of the word. So, سبک + است becomes سبکه (sabok-e).

When I hear the "e" sound at the end of سبکه, how do I know it means "is" and isn't just the ezafe linking sound?

Context tells you! The ezafe (the spoken "e" sound linking nouns and adjectives, like in معلم جدید) is almost never written out. But when the "e" sound represents the shortened verb "is", it is explicitly written at the end of the word using the letter ـه. Plus, grammatically, the second half of the sentence needs a verb, and سبکه sits right where the verb belongs.

The sentence uses او for "his". Is that the most common way to say "his bag" in spoken Farsi?

In highly colloquial street speech, Iranians usually use the attached pronoun suffix (-esh), making it (kif-esh) instead of (kif-e u). This sentence mixes colloquial verbs with slightly more formal pronouns, which is actually very common in text messages, informal writing, or polite conversation where you don't want to sound entirely slangy.