Does the free analytics plugin also track osclass pay promotions as conversions? Does it differentiate between each promotion type?

Plugin allows to easily integrate analytics code to your site, but does not generate any statistics.

Ok but is there a way to track payments made with Osclass Pay plugin? Or provide a list of event names used by Osclass Pay? Or even another plugin that can also track payments made with Osclass Pay?

you can get it from Logs page:
https://plugins2.abprofitrade.eu/oc-admin/index.php?page=plugins&action=renderplugin&file=osclass_pay/admin/log.php

for more advanced analysis you may just read directly from t_osp_log table

That's way to hard for me to do. It should work as default counting page views, scrolls, and all other events but when someone makes a payment it should set an event for each type of payments and we can set those events in GA as conversions.