1. All cron jobs scheduled in Magento are stored in 'cron_schedule' table in database, so we can check if the cron jobs 'catalogrule_apply_all' and 'catalogrule_apply_all_individual' are present.
This can be done by the following queries:
SELECT * FROM `cron_schedule` WHERE `job_code` = "catalogrule_apply_all_individual"
SELECT * FROM `cron_schedule` WHERE `job_code` = "catalogrule_apply_all"
We are expecting to find the records for these cron jobs with status="success".
2. If the rules were applied, we should see a discounts generated in database table 'catalogrule_product_price', with 'rule_date' field containing dates for the current day, next day, and the day before.