Regarding your questions, some kwick answers.
1. Aside from the ATP written test, will I need to do a Commercial written or any other test?
I think the ATP test will be enough, unless you want to exercise the commercial license.
2. Is it the DGAC that verifies your log book or LAN?
Your logbook is verified by the DGAC, to confirm your total hours with the training institutions.
3. How long does it take to get a date for a medical and psychological eval?
A medical can be requested for the same day, you can use the FAP or Tessa institutions.
4. In how long of a time frame can I get all of this taken care of?
It all depends on your own scheduling and follow up.
5. What is the approximate cost?
Do not know, you should confirm and budget accordingly.
6. How long after the interview do they normally let you know if you are hired and is there a time frame you are given before you start your training?
Different timeframes for different situations.
If looking for official answers, some of your questions should be answered by the local aviation authority, the DGAC. Since you are fluent in spanish (actually peruvian) you or some local contact can reach them via their local phone 615-7800. This is the link to their website:
MTC - DGAC: Inicio