Hmm… While working on proper convergence something sprang into my mind and I decided to test it.
I thought to myself that to recreate torus generatrix alone would be too little so I added outline lines too. It turned out to be good idea and now boundary layer is properly generated each time.
Just to the record (and to avoid language misunderstandings):
Unfortunately, one thing solved - another occurred 
In terms of the ball I did exactly the same thing as I’d done previously, but this time (because of some reason) it didn’t work.
I cut the sphere in three different ways, which was cut with a use of all three main planes.
1. Cut in half (single cut)
2. Double cut
3. Triple cut
On all three occasions, ball meshed together with torus resulted in no Boundary Layer. Why? I have absolutely no idea. But if it failed this way I thought to myself I could try to cut the ball in a way I would do preparing it to blocking.
At first I cut squares at each “side” – something analogical I did in terms of meshing a bow in torpedo-like shapes for instance. The difference is that here you have full sphere instead of a half one. But the basic idea was pretty much the same - that is to artificially cut the sphere surface in quadrilaterals (elements that have four sides). After a while (and few versions) I decided to leave it like this:
(Squares from all three main planes perpendicularly projected in all directions.)
Because this took me quite a chunk of time to work it out and make up my mind which version to choose I did another approach too. I just moved main planes at 50% of a sphere radius in each direction and made cuts.
(Main planes moved perpendicularly in both directions. | Cuts come from different combinations.)
Ultimately I selected two versions:
1. All six planes’ cut.
2. Billiards balls-like cut plus one cut with a use of a main plain (thin black line).
This time everything went smooth and fast.
In case you noticed it: I increased the Boundary Layer height to make it more visible. And because of that I had to widen the gap between both elements. Because of some reason with previous distance mesher was losing BL from sphere in this region. Maybe it’s because in this case BL’s final element would have to be bigger than elements between torus and sphere? Take a look at picture below and write if you have any idea.
STRANGE PATCHES
I think I know where they come from. While cutting and meshing this simple (and problematic) geometry I’ve noticed that sometimes when element size is bigger than a patch I cut the mesher does its own division. Look:
Cuts (I left the triads so that you could see sphere orientation):
And the mesh:
I guess this is the way that mesher defends itself from crashing. The question is however why - where there are no cuts at all - the mesher assigns particular element in such a strange way instead of creating more even and coherent patches. Anyone has any idea? And the most important: does it have an influence on results? Hmm… another thing to check. I’ll let you know.