Learn Hardcore Korean: najunge gongwoneseo gati sanchaekhalkkayo? - Shall we take a walk together in the park later?

It makes a polite suggestion/invitation and seeks the listener’s opinion, similar to “Shall we…?” With 같이, it clearly means “Shall we do it together?” Without 같이, -(으)ㄹ까요? can also mean “Shall I…?” or “Do you think…?” depending on context. Compare:

제가 도와줄까요? = Shall I help?
비가 올까요? = Do you think it’ll rain?

Why is it 공원에서 and not 공원에?

에서 marks the place where an action happens (at/in). 에 marks a destination or static location/time. Since the walking happens in the park, use 공원에서. If you want “to the park,” you’d say 공원에 가다, e.g., 공원에 가서 산책할까요? (Shall we go to the park and take a walk?).

Is 같이 necessary?

Not strictly. 산책할까요? already implies “we” in this suggestion. 같이 just makes “together” explicit and friendly. If you name a partner with 랑/하고/와, 같이 is optional but common: 너랑(하고) 공원에서 산책할까요? / 너랑 같이 공원에서 산책할까요?

What’s the difference between 같이 and 함께?

Both mean “together.” 같이 is everyday, casual–neutral. 함께 is more formal or written. Your sentence with 함께 is fine but a bit formal: 나중에 공원에서 함께 산책할까요? Don’t use both at once (e.g., avoid 같이 함께).

Can I change the word order?

Yes. The natural order is Time > Place > Manner > Verb, which you have. Variations are fine:

나중에 같이 공원에서 산책할까요? (also natural)
공원에서 나중에 같이 산책할까요? (okay but slightly less smooth) Keep 산책할까요 at the end.

How do 나중에, 이따가, and 다음에 differ?

나중에: later (unspecified; could be much later). Sounds non-committal.
이따가: later today/soon (same day). Very common for plans: 이따가 공원에서…
다음에: next time (another occasion), often to postpone: 다음에 같이 산책해요. If you mean later today, prefer 이따가 rather than combining 오늘 with 나중에.

How polite is -ㄹ까요? What if I’m speaking casually or to a senior?

Neutral-polite for most situations: 산책할까요?
Casual with friends: 산책할까?
Extra deferential/honorific: 산책하실까요? or 산책하시겠어요?
Preference-focused alternative: 산책할래요? (Would you like to…?)

Where is the subject? Does this mean “we”?

Korean often omits obvious subjects. Here it implies “we/you and I.” You can add 우리 to make it explicit and very natural: 우리 나중에 공원에서 같이 산책할까요?

Any pronunciation tips?

나중에: [na-jung-e].
공원에서: [gong-wo-ne-seo]; it flows like [공워네서].
같이: [ga-chi] (not [ga-ti]).
산책할까요: [san-chaek-hal-kkayo]; pronounce the kk in -ㄹ까요 as a tense, strong k.

Is 산책하다 the only way to say “take a walk”?

산책하다 is standard and natural.
산책 가다 is common in speech (go for a walk): 나중에 공원에 산책 가요.
걷다 means “to walk” (more general, less leisurely): 공원에서 같이 걸을까요? has a slightly different feel.

Why 산책할까요 and not 산책을 할까요?

Both are grammatical because 산책(을) 하다 treats 산책 as a noun plus 하다. In modern usage, the compound verb without the object particle is more concise and preferred: 산책해요/산책할까요 sounds more natural than 산책을 해요/산책을 할까요.

How do I accept or decline this invitation naturally?

Accept: 좋아요! 몇 시에 만날까요? / 그래요, 이따가 봐요.
Soft decline: 미안해요, 오늘은 좀 어려워요. 다음에 같이 걸어요.
Postpone/hedge: 좋은데 나중에 시간 될 때 해요.