Learn Hardcore Indonesian: Saya naik sepeda ke kantor setiap pagi. - I ride a bicycle to the office every morning.

saya means I (formal). The informal equivalent is aku. Yes, you can omit it when the subject is clear from context:
Naik sepeda ke kantor setiap pagi still means I ride a bike to the office every morning.

What does naik mean in this sentence?

naik literally means to go up, but with vehicles it means to ride or to board. It’s used with transport modes: naik sepeda, naik bus, naik pesawat. A more formal verb is mengendarai (meaning to drive or to ride).

Why is ke used before kantor instead of di?

ke marks movement to a place (e.g. to the office). di marks static location at a place (e.g. at the office). So naik sepeda ke kantor = ride a bike to the office.

What does setiap pagi mean, and where can I place it?

setiap = every, pagi = morning: every morning. Time expressions can appear at the start or end:
Setiap pagi saya naik sepeda ke kantor
or
Saya naik sepeda ke kantor setiap pagi.

Why aren't there words for a or the before sepeda and kantor?

Indonesian has no articles; sepeda can mean a bike, the bike, or bikes depending on context. Specify quantity with numbers: dua sepeda = two bikes. Or use reduplication: sepeda-sepeda = bicycles.

Could I say Saya mengendarai sepeda ke kantor setiap pagi instead?

Yes. mengendarai is a more formal verb meaning to drive or to ride. Both sentences are correct, but naik is more colloquial.

Can I change the word order without changing the meaning?

Yes. Indonesian is flexible:
Setiap pagi saya naik sepeda ke kantor
and
Saya naik sepeda ke kantor setiap pagi
convey the same idea.

What part of speech is sepeda, and how do I pluralize it?

sepeda is a noun meaning bicycle. To make it plural, you can reduplicate: sepeda-sepeda = bicycles, although plural is often implied by context without reduplication.