For (a),(b) pattern search don't forget that http://ps.waltheri.net/
does quite a great job.
For (c) you need to find a good dan bot, Leela https://www.sjeng.org/leela.html
is free for instance, Zen or CrazyStone do also a good job but are not free, and there are many others, see on the forum. Unfortunately all-in-1 software may be equiped with weak engines, so I would not trust the moves they recommend, a plus would be that your favorite tool accept input from GTP engines, so you can plug your favorite dan engine for analysis.
For tsumego, I'm also in search of such an application. I use MadLab http://www.t-t.dk/madlab
it generally does a good job, but it is also often taking ages to answer...
I heard XuanXuan http://www.xuanxuango.com/index.htm
go does a fine job too, but I never stepped to buy it (mainly because I was discouraged by this obscure chinese website).
I tested also Panda Sensei https://play.google.com/store/apps/details?id=pandanet.tsumego&hl=fr
because I was thrilled about it, being victorious in the tsumego championship against top pro pairs http://www.pandanet.co.jp/event/PandaSensei/index_e.htm
, but clearly the Android version is NOT the real deal. Plus you can only use it for free at the beginning, after solving a few tsumegos you have to buy Panda points. At first I was pleased by its solving speed, but the total lack of ko options and the illogical choice of "inside stones" makes it unusable in practice (this is only my opinion), so I gave up. Apparently, the killer version was kept as secret as alphago.