Executrix Fleet Mastery Technique Confirmation?

No, the fleet mastery events are only to get 6* capital ships to 7*. You only get to do it once a month unless you pay to refresh. It's 2 million credits to promote a cap ship from 6 to 7, not to unlock. I'm not sure how you got everything so mixed up.

So, without buying packs and only buying refreshes, how long does it take to get the shards needed for 7*? (in months). Looking for confirmation of refreshes per event.

Ok,

You can refresh once per event , the event is once per run time, you can only access the event once you have six starred the appropriate cap ship via the original method which is available several times a week.

You unlock capital ships by events that open automatically I'm lower levels. Can't remember the start level you unlock, but I think it's 3*.

To star them up, you have challenges in the ships area. The challenge to upgrade each capital ship is available when the normal challenge requiring it is available - Tuesday and Friday for AA, Wednesday and Saturday for Mace, Thursday and Sunday for Tarkin, all on Monday. This allows you to get the ship up to 6*.

One a ship is 6*, you get access to the fleet mastery event for that ship. These events come one a month and give 15 shards each time. You can refresh with crystals once each time. This allows you to get the shards to get the ship to 7*.