If you did well in A-level Maths or equivalent relatively recently then you'll find MST124 quite straightforward, although some of the material will be new. I'd probably suggest you take both simultaneously. There is a specific "route" through the modules if you are taking both at the same time, in terms of the order in which you learn the material, and the deadlines for the assignments are structured in such a way that you can follow the syllabus in a linear fashion (you sort of move back and forth between each module depending on the topic(s) as you progress).
If you are very unsure of your background then you could start with MST124 then start up MST125 in the February session, which would give you longer to consolidate the earlier material in MST124 (and also means the exams would be taken in separate exam periods). If you had an A* in A-level Maths though I'm pretty sure you could easily manage both at the same time. The exams for those modules are a lot easier than the A-level exams generally, as you get to take the handbook in with "special annotations" (basically, you can write any notes you want that will fit on the pages of the handbook), and the exams themselves are multiple choice which makes some questions more straightforward (although it does mean you have to be careful with your algebra while more involved calculations as there are no method marks).
As far as what will be needed for the conversion, I couldn't really say, it would probably vary depending on the course. I'd suggest contacting the course provider and asking about what prior knowledge would be expected and/or useful. To my knowledge AI involves a fair bit of stats, and otherwise is a lot of control theory/systems engineering as I understand, which is elements of calculus and differential equations (how far into it they go can vary a lot though; a fully rigorous mathematical treatment could entail proper analysis, while they could also take a more practical approach which is a bit more handwavy).