You can only level up the mine three times, max output is 15 per day. Using only those, it would take 60 days of saving for a pack of 11 ancient shards for 900 gems, but of course you're not using only those - you should also get some gem rewards on a daily basis from clan boss, daily quests and so on. 

In any case you don't need to wait longer than 180 days before getting a solid Lego, because that's when you get Scyl from login rewards. Unfortunately most of the epics from login rewards before Scyl, other than High Khatun, aren't that useful - probably Dark Elhain is the best of the lot and she's merely decent. 

No, the mine plus doing the advance quest, yield about 25 gems a day, so every 12 days you get three ancient shards, if they'd fix the mastery system to cut the prices of gems to how many mastery's you need you'd save for mastery's included, but for mastery's or a ten pack that would be about 30 days in total

I like that you have your Goldens in your photo.  I was into Brittanys for training and fostering.  Dogs RULE