I'll try to explain a bit more in detail.
1) I mean the draw screen, bottom right corner.
If explicit value is used for QualifDraw, the correct size is only shown when going through "Tournaments of the week" option (and also when draw appears automatically during the week).
If you access it later through "All tournament draws" screen and select the tournament in question it works only when -1 or -2 values are used.
You can easily see this if you set Sydney and Hobart to 30 main draw size and set Category07 QualifDraw to 32 instead of -1.
Just check the draws during the tournaments and several weeks later and you'll see the difference.
2) not exactly, the first week example only shows it obviously, it is not possible to cycle at all since there are no older draws than those of the last week.
But all the time the current week tournaments are shown and selectable through "All tournament draws" screen but it is not possible to cycle through them.
If you try next tournament arrow the week changes to the one before and you cannot return to the last week qualifying draws unless you exit the draw screen and select another tournament directly.
It seems the current week tournaments are not included in the list when using next/prev arrows.
I think it should be possible to cycle through the current week tournaments qualifying and the main draw should say there is no draw yet just like when you select such tournament.
In fact I think it would be better to show the empty draw with message than to omit the draw completely even in the case the tournament has no such draw at all, e.g. no qualifications.
Similarly to the case when tournament has no doubles draw, it is always shown though empty.
3) again not exactly as I see it. I'll give some examples and observed behaviour to clarify.
-1 value says the qual draw size is the same as the main draw, rounded up with regard to number of Q rounds (it works this way for a long time)
-2 value says the qual draw is half the size of the main draw, rounded up with regard to number of Q rounds minus 1 (should also be Q, not Q-1)
Ex.1: 32,30,28,26 main draw sizes with -1 QualifDraw and 3 Q rounds all result in 32Q, multiple of 8 (2^3) CORRECT
Ex.2: 64,62,60,58 main draw sizes with -1 QualifDraw and 3 Q rounds all result in 64Q, multiple of 8 (2^3) CORRECT
Ex.3: 60,58 main draw sizes with -1 QualifDraw and 2 Q rounds both result in 60Q, multiple of 4 (2^2) CORRECT
Ex.4: 64,62,60,58 main draw sizes with -2 QualifDraw and 3 Q rounds all result in 32Q, divided by 2, mul of 4 and 8 (2^2 and 2^3) ONLY RESULT CORRECT
Ex.5: 64,62 main draw sizes with -2 QualifDraw and 2 Q rounds both result in 32Q, divided by 2, mul of 2 and 4 (2^1 and 2^2) ONLY RESULT CORRECT
Ex.6: 56,54,52,50 main draw sizes with -2 QualifDraw and 3 Q rounds all result in 28Q, div by 2, mul of 4 (2^2) INCORRECT, should be multiple of 8 (2^3)
Ex.7: 60,58 main draw sizes with -2 QualifDraw and 2 Q rounds both result in 30Q, div by 2, mul of 2 (2^1) INCORRECT, should be multiple of 4 (2^2)
All these are examples of the actual behaviour of the game engine at present so it rounds up the values for sure.
-2 value should have the same calculation formula as -1 value except the additional division by 2 in the beginning of it.
Now it seems not the case, maybe the division is done after the rounding up instead of before, that would have the same incorrect behaviour.
3a) still applies for -2 value, the qualifiers are ignored, there is no one with [LD] flag and wildcards are sometimes given to foreigners.