Hi there,

Let me start by answering your questions at face value, but further below I'll give you some advice.I

1. Your perception is correct. Issue tree takes much longer to explain, and usually all that explanation is unnecessary. So you should go for the math function as it is more efficient and easier to explain. The exception is when you are struggling to find the function (then you have to use the issue tree to get it, but in the end try to convert it to function).
2. As a general rule you should separate them, or at least separate the structure from the assumptions and calculation. The reason is simple: communication is more clear, and it is a more reliable approach (less mistakes). It is common to have a lot of discussion around assumptions. If you mix assumptions with the structuring (particularly when the interviewer is still unsure that you'll get the structure right), then you risk being drawn into discussions and lose track of the function you were trying to build. It is also tougher to receive a hint if you are getting something wrong in the formula…

The real question here is: if you perform the same tasks in a different order, howcome do they take longer?

The answer usually is… overexplain things. When doing everything together you just over explain once. When doing separate, one does it multiple times… 

What one needs to understand is that a good math formula does not need a lot of explanation. Usually the only thing that needs a longer explanation is for e.g. a segmentation (if the formula requires one). Once you have a good formula, it should be quite straightforward to go (almost mechanically) through assumptions, chosing a number, giving one backup reason, and asking for agreement. This should be actually faster than the alternative (unless it is a very simple market sizing exercise).

Hope you review yourself in this comment, but if not, I am happy to further discuss in private.