What services must I leave switched on in Elysia cron I have installed Elysia Cron to import some Feeds data periodically.
However, I have switched off all the other cron tabs that I have in order not to interfere. However, my database size grows to ten times the size as when the cron was switched on without Elysia cron.

Must I switched them on and with what periodicity?
Elysia cron is just an improved durpal cron service. You must have enabled the services you have enabled by deafualt in the standard Drupal cron. Some of them, for example, remove temporal data from the database (probably the reason your database is growing). 

So, yes, you must have the services enabled, and those are the services enabled byu default by Drupal. Obviously the exact services that must be turned on depends on each installation.