Sakura's gift is good only when you get #1 rank rewards. Which means its pretty much useless event, except for free 35 packs you can get during whole week, which usually get you 10adv refines~. If you value your coupons/money, avoid spending there. IIRC there was only one time when something wasnt overpriced (susanoo sasuke frags, only one time ever).

If you are interested in buying adv refines, treasure of the sages is the best event there is.

Garv, that depends on current levels of each function. You are generally right, although cave keys require focusing on charms (at least 6-7lvl on each ninja you want to have better cave runes) to get the most of it. Refines are more balanced, since they give some of each secondary stat and gold purification is generally easy to make on 1 attribute of choice (example: you want ini, you roll until get ini and even reroll other gold ones, then its up to rng which 2nd one you get and from this point it gets expensive). Essences seem to be the way to go up until lv15, since iirc thats when 1 golden essence isnt enough to lvl up. If all of the power functions are on rather mediocre level, essences undoubtedly provide the fastest initiative boost.

OP asked which event is good place, so mentioned events are the answer. If OP wants to get most stats the cheapest way, nobody on forum can provide him 100% accurate answer- op needs to calculate how much power each stat gives (check character stats, remove cave rune/mangatama and see how much power X ammount of stat gives) then calculate cost of items and how much stat they give and see what has better ratio. Also after each thing levels up, it's diminishing returns usually are higher, so you need to recalculate because results will be slightly different (i recommend doing it in excel- easy adjustments).That method is painstaking but allows one to develop their account in the most optimal way. I personally never bothered with it. However since you will upgrade everything (one day) anyway, whether you do this first or second it doesnt make THAT much difference. You honestly cant go wrong with using rebate with it's maximum efficiency, even if that power source isnt the most optimal :-)