Sweep all the ninjas! Seriously, I sweep ninjas all the time to refine. I actually prefer week 4 to week 3 because I've been sweeping ninja fragments to get as many points as possible.

It is a huge amount, only doable if you've saved around 40-50 stamina potions, or can buy stamina with ingots.

Well, that's the point. Personally, I think using stamina pot is a waste unless there is some kind of weekly event for sweeping. We have a goldfish event this week, but...:L
Anyway, we also need a good amount of awakening material, and material to upgrade gears.. For some reason, even when you clear exam lvl 120, black market still gives kage material occationally which is totally useless..

And, if you are sweeping for refinement, not all ninja should be sweeped, since not all of them give same amount of points. Guy-Asuma-Kurenai etc should never be sweeped after 5 star, since they only give 2 points. And those who does give 10 point, well it's are a bit hard get them to 5 star..

Sweep to get ninjas 5 stars (at least those who you play most) you will need that update later.
Or for points like Niji said if you already have them 5 so its ok..

This goldfishing event doesn't make any of the stamina use feel anymore worth it than the 60 stamina does. Dx The rewards are incredibly expensive for minimal return. One day, left off with 86 points I think, not even enough for a single Neji fragment

I always sweep ninjas by their points - 10 first, 5 second, 2 last. Just because they're 2 points doesn't mean I leave them alone ;P - if I can do them all everyday then I get around 1.5k fragments by the end of the week. Not counting any I may get from Survival/Treasure. Then I do 4* and 3* ninjas. But that's just my own personal system since I'm trying to get my Iruka starred from the refinement.

This week I sweep upgrade material and awakening material
Next week I'll sweep all ninjas. Ultimate goal is make all sweepable ninjas to 5 stars and prepare for the ninja star system. Also the reward from refine fragment will change overtime. Now it maybe Iruka but later will be someone else according to CN version and even more rewards, not just seal and summon scrolls.
Also ninja like Neji who is better than his GNW version with skillbook upgrade will require a huge amount of fragments. 100-150 frags for 1 skill upgrade if I'm not mistaken.

No, you only need 20 to 30 stocked beforehand if you do things right, those are not counting the ones you get and use during the event thou, just stock.
Unfortunately, my more detailed explanation got eaten by the forum, I am not writing them again.