1) Don't bother learning all of further maths. So much of it is centred around integration, which is almost completely ignored in 1st year at LSE - 95% of the course is about differentiation and the other 5% is simple integration you're already familiar with from C4.
What you should learn is the part on matrices and vectors (all of it apart from the geometry related questions related to calculating volume/area). This will prove to be very useful indeed. Don't bother with anything else including complex numbers.
2) The main reason people fail MA100 is that they don't keep up with it week by week. It's the type of course where if you get lazy 1 week, then you can quite easily be lost forever unless you spend quite a lot of hours catching up in 1 go (which a lot of people don't do because they get carried away with the fun part of university life I guess).
Another reason why people fail is that they don't do the homeworks - they find the solutions, copy them and hand them in. Then each week they get a "very good", so they fool themselves into thinking that "I'm doing ok in the course, I can kind of follow my classes, I'll learn it in the holidays". When the holidays come, you realise just how much stuff there is to learn and it becomes so daunting that you basically give up. I've heard of people with 90%+ marks in A-level further maths scoring 45% in MA100 for this reason. It's not to do with being smart/your A-level background, it's all to do with keeping up week by week.
I think the MA100 exam is actually really predictable, you just need a good memory + you just need to put the hours in. It's not that many hours anyway, probably like 2 hours of lectures + 1 hour of class + 1.5 hours of independent study each week. Hardly a lot when you only have 12 hours a week of lectures + classes.
3) EC102 has almost no maths in it, nobody fails it because they're weak at maths (on the rare occasion, you'll have to solve a quadratic, that's about as hard as it gets).
It's hard to say why EC102 is so hard, but it's a lot to do with not understanding how to apply what you learn in lectures to the type of questions you're asked. Quite often, sitting there even with all your notes + books, you have no idea how to start a question. It can be really frustrating and it's a big test of character (a lot of people just give up if they can't see how to do begin the question within 2 mins).
The way I did well in this course was by going to office hours every week in the 2nd term + reading the solutions to the questions over and over and over again. The solutions are good because they not only explain how to solve the problem but actually all the theory is first explained there. Most of what I learnt was from the solutions - I more or less ignored the lecture slides for a long time. I would just sit there and memorise the solutions (moreover, I tried to understand HOW the solutions were constructed, i.e. tried to understand the thought process).
If you've not done A-level economics, go and teach yourself the microeconomics parts of A-level. Don't bother at all with macro.