Your old passport is invalid once the new one is issued, it's only purpose now is to confirm the same passport number the visa was originally issued to is yours. All stamps will be in the new valid passport. Printout a copy of your DTV as well for the passport control officer.
Anonymous participant 6 months is cutting it close these days. Times have changed and requirements are getting somewhat stringent. Possibly a cover letter along with your application stating your reasons for visiting, why this course , general interest in why you love Thailand, plans after finishing the course, and what you'll do with the remaining 4 years of the visa.
Manually edit the biodata info. Do not trust the OCR to read and fill the fields correctly, as warned about on the evisa application website. You can edit up until the time you submit. No mistakes are allowed for the biodata entry fields.