Dün gece geç saatlerde pasaportumu kaybettim; sabah panik içinde gümrüğe giderken trene yetişmeye çalışıyordum.

• Dün gece by itself means “last night.”
• Adding geç saatlerde (literally “in the late hours”) specifies that it happened at a late time during the night rather than earlier.
• The plural saatlerde implies an unspecified range of hours (“around late hours”) rather than a single exact time.

Turkish marks definite, specific direct objects with the accusative case suffix (one of -ı, -i, -u, -ü). You already have the possessive -um (“my”), so you stack the accusative -u on top:
pasaport + -um (my) + -u (accusative) = pasaportumu (“my passport,” definite, as the thing you lost).

• kaybettim (I lost) presents the act of losing as a completed event at a specific point in the past.
• kaybediyordum (I was losing) would imply an ongoing process or repeated action, which doesn’t fit here because you lose something at a distinct moment.

• In Turkish, like in English, a semicolon links two closely related independent clauses.
• Here, it emphasizes the connection between losing the passport at night and the next-morning panic.
• You could replace it with a period or a comma plus ve (“and”), but the semicolon keeps the clauses tightly connected without adding a conjunction.

• içinde means “inside” or “within.”
• Figuratively, panik içinde = “in panic” or “in a state of panic.”
• You cannot say panikte; that would sound like a very rare noun form. The standard expression is [emotion] içinde to mean “in a state of [emotion].”