pokerface

This should be enough, for example my college (Trinity Hall) lists the following requirements: http://www.trinhall.cam.ac.uk/prospective-students/undergraduates/courses/detail.asp?cat=Natural%20Sciences&ItemID=1614.

To me it sounds quite economics-y because there is no experimental research involved so it would be hard to classify it as science (however, the EE guides permit science EEs based on data found in some kind of sources but personally I wouldn't recommend it). Remember that an EE cannot be multidisciplinary so when you decide which subject you want to write your EE in you'll have to focus solely on the aspects of your research question related to that subject.

International students always have to prove their proficiency in English and usually IB English is sufficient but if you don't study English as a subject then I'm afraid you'll have to take TOEFL/IELTS.

For SL you would already be required to know some German.

In exactly the same way as you do before the results - through UCAS, only in such a case you have to specify the grades you got and that's the only difference.

What you've just described is a conditional offer. Unconditional is when you apply after you find out your results and the uni accepts you without any further requirements.

Maybe, but my friend applied to study Maths at Cambridge with only Polish-school maths which doesn't involve any of the elements included in Further Maths and got an offer. However, if you apply for CompSci with Maths, which is the most popular option, you will most probably have to take STEP and that's why they don't care that much about the kind of maths you do at school because STEP will sort things out anyway.

I'm serious, IB Maths HL = A-Levels Maths + Further Maths (more or less) and Cambridge is aware of that. I didn't take Further Maths (because as most of the IB schools mine also doesn't offer it) and I got into Cambridge to study Chemical Engineering. After you apply you also have to fill in a special 'questionnaire' called SAQ and in it you get the chance to explain whether you were unable to take certain subjects that you might have wanted to. So don't worry and apply, Further Maths is not an obstacle here.

Cambridge treats IB as equal to A-Levels, we are at no disadvantage. And there is no need to do IB Further Maths, that refers only to A-Levels.

All unis only required a specific grade in English from me and I took English B, so I guess in your case that's even more unlikely that they will want you to take TOEFL/IELTS.

If you want a highly maths-based option, go for relativity - some of the concepts may be a bit non-intuitive but the calculations are quite straightforward and most of the topic is about calculating stuff.

Unis don't care about maths if you're applying to study languages.

My friend had an offer for engineering at Oxford which was 38 points but with 7s in Maths and Physics which is probably harder than 776 because then you can mess up one of the toughest subjects.

It's usually in the 40-42 range with 776-777 at HL.

One college (King's) gives quite low IB offers - 38 points with 766 at HL so if your interview went well you could be accepted. At other colleges it's 40-42 points with 776/777 at Hl, so if you're not willing to retake any exams, then King's is your only option at Cambridge. On the other hand, even at King's they may specify that the 7 is in Maths (they don't have to, my offer from a different college was 776 in Maths, Physics and Chemistry in any order but sometimes it's specified) and in that case unfortunately they wouldn't take you. I would advise you to do some research about standard off