How does week rank compare to day rank?

Good question! I would say everything is important, weekly rank could look better than a daily one or vice-versa. Someone who has already launched can actually give a better insight, we just launched for the first time today!

I think week rank is probably the least important unless you really care about a badge :) But monthly rank can help you stay visible for longer in the product section on the website (not so much on the app). Also, another organic boost can come from the Golden Kitten awards in the end of the year. If your launch goes well and you get the results you're hoping for/leads/clients/registrations/etc — you can always launch paid promo for your product on PH. Organic launch is a really good way to see if the ads would make sense. PH offers a self-serve ads platform, so you can even calculate ROI in advance.

Yes @zack_anselm , even after launch day it is advised to keep the momentum.

I'd imagine if you get week rank you'd get day rank as well Not sure about the benefits, but I'd imagine it's significant