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GoldenBeetle
Ah yeah, Alyssea has a better idea than me, but since I am on PST (which is the same as FR site time), that is the only frame of reference I can provide. Which for me, the jewel summon chance is 12:00-14:00, and rollover at 0:00. This may or may not differ depending on your own timezone. ^^;
(Fortunately, Otogi has built in countdown timers so it's not difficult to figure out when this or that is live for you.)
For grinding, right now you should have the minor magatama dungeon unlocked which drops 1-2 star magatama. Once you hit level 10 on your player level you unlock the medium magatama dungeon which drops 2-3 star, and the major magatama dungeon at level 20 which drops 3-4 star.
Here's a list of the different daily event dungeons, what they drop, and what times they are open/level unlocked.
http://otogi.wikia.com/wiki/Daily_Events
Also, regarding the current event "Chopping Trees? Stop, Please!" I'd say just ignore it/don't worry about it. Otogi has monthly events which come in two flavors, Tower and Conquest.
Tower is simply a story mode event. You complete chapter sections to progress and while they are long, they are generally more newbie friendly.
Conquest, which is what this current event is, is 'fight the raid boss' style. You have to beat the boss, which comes back at higher and higher levels. You need a good amount of prep in order to do these efficiently and in general is very overwhelming for newbies.
I'd say, just skip it. I skipped my first event as well because I simply wasn't established enough for it. Besides, there will always be more in the future. c: