I needed to book two Delta seperate tickets for a flight to Korea. My Delta domestic flight arrives at LAX at 6pm and I need to depart from TBIT on a Delta Marketed Korean Airlines presitge airlines(Business class per Flight agency) flight at 1040 pm to ICN. I will only have carry-on luggage. The reason I booked two flights, is so I could stay under budget for the business class flight. My questions are noted below:

1. Will I be allowed to check into my International flight 24 hours prior, or will I need to wait until my flight is completed at 6pm at the LAX airport before checking into my International flight?
2. If I need to check in for my Korean Airlines flight after I land at LAX and show passport, etc.. What is the best way to get to TBIT and check in for my Korean Airlines flight?
3. Should I link my two seperate flights via the Delta Diamond line or not?
4. When I return from ICN to LAX later that week, does anyone have tips or suggestions upon arrival at TBIT and catching my Delta flight at terminal 3?

Thank you in advance for and assistance you are able to provide.