HOWEVER, you may not be able to *check domestic luggage* at the International Terminal. Not all airlines will have counters there. I don't know if Delta will allow you to check domestic luggage at their counters there. You will have to take the (slow, crowded) airport shuttle over surface streets to get to the domestic terminal to check luggage. If you are not checking luggage, yes, you can access domestic gates from the international terminal.
Yes you can, you just need to go through security and ride the train to your terminal.
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