In my experience, if the handicap is correct, there is no need to induce mistakes from your opponent. It's very possible to win just by taking advantage of your opponents mistakes.
For me, the goal of studying L&D or tesuji is to be able to start reading a position correctly without having to read very much, or get a better intuition of where reading would be valuable. It has to do with making your reading more efficient, not necessarily being able to "know" the position right away (although "knowing" does seem to happen for a lot of common positions and some uncommon ones with enough study.)
As for why you don't feel like you are improving even while studying problems, it would help to know your studying methods (how long do you study, when do you consider the problem solved, etc.)