VS,
Integrated versus Modular as suggested earlier has been discussed at length. Check the search option. Its an argument that keeps running. If you get called for the interview and theres people from both camps there the company has decided its down to the individual on the day so dont worry.
Yes you can get a job without a type rating, but you'll have to do one before you can fly with the airline.
Normally the airline will offer you the job first and then you'll get your rating through them. Some make you pay for it (Ryanair), some give it to you for "free" (ahem) and bond you for a number of years (the 'old' way of doing things)...and some do both !!(Ryanair again !!)
If you go get a rating before youve even spoken to the airlines the chances are it will have expired long before you get your first job. In my opinion its not worth the expense.
You'll get 20 hours on a jet simulator anyway as part of your MCC which will prepare you for the sim ride you'll need to pass as part of the airline selection process. And remember if you have a type rating already the examiner will be expecting you to be hotter than the other wannabees when it comes to your sim check / interview for the job !!
Mathematics is 'O' level stuff at best, the same with the physics. You can go into it further but basic Albegra will get you by. I was and still am cr*p at maths. I didnt do physics in school, opted for Biology instead !! But I passed all the atpls first time so dont worry too much. Memory, lots of hard work and a bit of luck gets you through.
Best of luck....
T