I am from Germany, so do not wonder when my English isnt up to a native English speaker standard.
I found this site by chance, as I was looking whether the anime series is worth a try. As I saw that the source for the anime was a game and that there is a guide for it, I tried the game instead, even altough I cant speak Japanese. With Rikaikun und this guide is it somewhat doable even if there remain many mysteries, since there are no answers for many questions...
For example (unsorted): What does a memory ticket do? - You can use it to get more story of that specific girl (unfortunately, audio only...)
How do the study missions work? - Its a duo battle. As a partner one should choose one who is at least in the same or higher in the hierarchy of Cool > Pop > Sweet > Cool and has high atk points. So for example for Pop mission choose Cool partner or if no Cool or the Cool have bad atk points, choosing Pop partner is okay, too.
Is it possible to change the members of the own study group? - To change the member go to http://vcard.ameba.jp/s#study/deck/edit/1 or click the お勉強ガールズの編成 link at the study page. The オススメ編成 button is for the auto selection. (Hm, I wonder if I should use the overall best choice, the respective best choice for cool, pop or sweet )
For which cards is it worth to level them max before a merge. - I'd consider leveling HRs/SRs to max before a merge, since those are the girls that have the most potential to have the highest stats in your deck. I 4MAX/3MAX most of my cards of rarity HR and above.
Are the photo cards limited to only a 3 times completion? - I think the answer is yes, only three times and you can only get it from the area mission...
Does every girl have her own jobs?