Learn Hardcore Filipino: Kailangan kong magtrabaho bukas ng umaga.

Kong is ko + the linker -ng. Ko means “my/I (genitive),” and the linker connects kailangan ko (my need/I need) to the verb phrase magtrabaho. Literally: “My need to work tomorrow morning.”

Can I say Kailangan ko magtrabaho without -ng?

Yes in casual speech you’ll hear Kailangan ko magtrabaho, but the standard/most natural written form is Kailangan kong magtrabaho with the linker -ng.

Why is it bukas ng umaga and not bukas nang umaga?

Use ng (not nang) to link a specific day with a time of day: bukas ng umaga, kahapon ng hapon, sa Lunes ng gabi.
Use nang mainly for adverbs, “when,” “so that,” or before verbs/adjectives (e.g., nang mabilis, nang dumating siya).

Can I say bukas sa umaga instead of bukas ng umaga?

You’ll hear bukas sa umaga, and it’s understood, but the idiomatic pairing for day + time-of-day is ng: bukas ng umaga sounds more natural.