Check expedia.com, it sometimes has negotiated fares available for foreigners that are available only on Expedia (the US version of the page).

You won't have any problems with online check-in on Latam. As for the ID check on Latam: It seems that they normally don't check ID's during boarding; they only scan your boarding pass. Your ID is verified at the security checkpoint, but the people who work there aren't Latam employees.

Of course you can't check any luggage, and it's also a good idea to come to the airport with a printout of your boarding pass (sometimes the check-in kiosks at the airport don't work). You can check in and print boarding passes earlier, at Latam city offices.