Tango01,
You don't have to convert your ICAO license into Chilean one before applying.
The minimum requirements are ICAO CPL and at least English Lvl 4.
After passing the selection process, LAN is going to sponsor you for the license conversion in Chile. As far as I know it only takes a multiple choice exam based in the FAA ATPL questionnaire, Glenn or AsA should be OK.
You should also pass the ICAO English Lvl 4 exam in Chile, the Chilean Aviation Authority doesn't take into consideration your foreign license English certificate.
All this process is taken during the Indoctrination/Initial training in Santiago de Chile before flying the SIM.
About the Psychometric, the best answer I can give you is be yourself.
There were many who prepared themself using the service of a Psychologist in LIMA and the answers were all the same...of course they passed the test but LAN found the trick and all of them were failed.
I don't know about the sim evaluation in Chile, but in LAN Argentina is taken using a Flight Simulator 2004 choosing the B737 Classic airplane.
As far as I know LA is not using the A320/B767 SIMs for the evaluation