Learn Dutch: Is mijn eigen parel verkocht? - Has my own pearl been sold?

This is the Dutch present perfect passive. While English forms this with "has been" + past participle, Dutch simply uses the present tense of zijn (to be) + the past participle. You don't use a form of hebben (to have) or add a word for "been" (like geworden). Therefore, is verkocht correctly translates to "has been sold".

Parel is a de-word. Why doesn't eigen get an -e ending after mijn, like in mijn mooie parel?

The word eigen (own) is a strict exception to the standard adjective inflection rules. It almost never takes the -e ending, regardless of whether the noun is a de-word or a het-word. You will always say mijn eigen parel instead of mijn eigene parel.

Why doesn't the past participle verkocht start with ge-?

Verbs that begin with an unstressed, inseparable prefix, like ver-, be-, ont-, or ge-, do not get an extra ge- in their past participle form. Since the infinitive is verkopen, the past participle is simply verkocht.

Why are the verbs is and verkocht separated by the subject?