When I'm talking about habit or custom, can I say:
"The king comes on Sunday and goes Monday."
without using the preposition "on" before "Monday"?
When I'm talking about habit or custom, can I say:
"The king comes on Sunday and goes Monday."
without using the preposition "on" before "Monday"?
Both Riley Francisco and HostileFork have given you different answers. In my opinion, I feel leaves on Monday sounds more correct than leaves Monday. Similarly, arrives on Sunday sounds better than arrives Sunday.
This does not mean that people will still omit the word on.
I believe people will understand the meaning you are trying to say without using the preposition. However, a preposition simply enforces the meaning you are trying to convey.
Using a preposition before a day of the week is grammatically correct.
Omitting it is common for American English speakers.
As everybody else says, your sentence doesn't read very well because it's not consistent: the two days should be treated the same.
Speaking on behalf of British English speakers, I think that with a preposition is clearer.
"The king comes on Sunday and goes Monday."
The main problem with this sentence is "goes" without saying where. Changing it to say "and goes on Monday" doesn't help it very much. Being more specific helps:
The king comes to town on Sunday and goes home Monday.
That would be fine, as would:
The king comes to town on Sunday and goes home on Monday.
As I mentioned in a comment, it's fine as "The king arrives Sunday and leaves Monday" or "The king arrives on Sunday and leaves on Monday".
I can't speak to whether there is a bias in British or Australian English to think the first sounds strange, but the second normal.
You'd very commonly hear someone say either "Why don't you come over Sunday?" or "Why don't you come over on Sunday?" But one exception I can think of would be if a specific time were named, you'd need the "on" before the day. This would not sound normal:
Why don't you come over at 12:00 Sunday.
You'd need to say "at 12:00 on Sunday".