*Gospel Library (or LDS Music).
LDS Tools has ward and stake information and doesn't have any hymn content.
Yes, just a few months ago, in fact, the Church got permission for 5 more hymns (All Creatures of Our God and King, If You Could Hie to Kolob, I Saw a Mighty Angel Fly, For All the Saints, and Be Still My Soul). They are already out in LDS Music Android and will be coming to LDS Music iOS, Gospel Library iOS, and Gospel Library Android with the next app update for each. (I think Gospel Library Windows, too.)
Some hymns we have been specifically told no for publishing digitally (at least one that I know of), and other hymns require a per-use fee (which the apps and LDS.org don't have any model to support). But the Church follows up again requesting permissions from time to time.