Apologies for the late response.
I am not exactly sure how the working would change if the forces were not constant, although I know you could not use the methods in the answers.
So this question is nice because it essentially broadens your decrement understanding (although the hard way of having to think about it a bit).
Think of the decrements as monsters in a room with you. There are 3 monsters, Lapse, Death and CI diagnosis. By referring to my timeline in the PDF attached, I have shown how these monsters interact. Lapses occur only at the beginning of the year and before the other monsters. After Lapses chooses what do do with you, the other monsters come in and have to fight with each other over what Lapses has left behind. In this way, Lapses can be treated as independent, while Death and CI diagnosis are dependent on each other (they occur at the same time).
As a result, we split the timeline into 3 components, 1 - before any decrements occur, 2 - after Lapses occur, 3 - after all decrements occur.
With question d, q50(l) = (aq)50(l) because this monster works alone, so only q50(m) and q50(c) are ones in which we need to use our multiple decrement formula for (see PDF). We need to use point 2 on our timeline as these decrements start after our Lapses, so technically, at the start of when these decrements occur, we need to have incorporated Lapses already. So lives outstanding will be 10 000 - 1 000. The rest of the math follows in the PDF.
Hope that helps
Hotseat - Decrements.pdf (0,7 MB)