Regarding your first question, if you can find it more comfortable to meditate lying down in bed then I see no problem with it. I've known a few people over the years who meditate this way. I've tried it myself but I usually fall asleep :)

Though if one is sticking precisely to the official rules of The Master Key System then you should really do all the exercises in the same chair because I think the author, Mr Haanel, is trying to set up an association in your mind between that chair and the mental states you achieve while doing the exercises in that chair. He hints at this in later lessons.

I would say it's a matter of personal choice really. That book was written in the early 1900s and there is much more success literature and information around now than then. If I was working through the book today, I would just set up an (NLP) anchor for myself regarding achieving those mental states so I could just re-trigger the anchor whenever I wanted to be in that "state of mind" in any location rather than relying on returning to that physical chair.

I think that's a more elegant modern-day solution but if you want to work through the book precisely as intended then I don't see a problem with it.

There is more information about meditation posture in What is the importance of Meditation Posture?

Regarding your second question, it is not possible to "let go" of something if you are focused on the thing you are trying to let go of. It's like trying not to think of a Pink Elephant...see, you just thought of one :) Since it's not possible to focus on two things at once (multi-tasking is just fast switching) then focusing on positive thoughts must mean you are not focused on negative thoughts.

So my interpretation of that exercise is that focusing on positive thoughts instead is fine. There is more information in Master Key System, Exercise 4: I can't seem to get certain songs out of my head. Am I doing something wrong?