yes. Easiest to hand over a copy of the visa, less likely to get mistakes. Check your stamp before you leave the desk. It doesn't hurt to carry the course info, unlikely you get asked but you never know.
You go to the Thai immigration where your TM30 is registered and file the TM47- 90 day report. It doesn't affect the time you are allowed in Thailand which is 180 days on a DTV stamp. All long stay visas, except the LTR, requires the visa holder to report where they are every 90 days. After you successfully file the first one, you can do them online. Numerous posts about it today